For triangle XYZ, m∠X = (2g + 16)° and the exterior angle to ∠X measures (4g + 38)°. Find the measure of ∠X and its exterior angle.

Answers

Answer 1

The angles in the triangle are as follows:

∠X = 58°

Exterior angle of ∠X = 122°

How to find the angle of a triangle?

The sum of angles in a triangle is 180 degrees. The sum of the exterior angle and the interior angle of a triangle is 180 degrees.

Therefore, let's find the measure of ∠X in the triangle XYZ.

Hence,

m∠X = (2g + 16)°

The exterior angle of m∠X  measures 4g + 38 degrees.

Hence,

2g + 16 + 4g + 38 = 180

6g + 54 = 180

6g = 180 - 54

6g = 126

g = 126 / 6

g = 21

Therefore,

∠X = (2(21) + 16)°  = 42 + 16 = 58 degrees

Exterior angle of ∠X =  4(21) + 38 = 84 + 38 = 122

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Related Questions

NEED THIS ASAP WILL GIVE BRAINLIEST HELP!

Answers

Answer:

D. Alternate Interior Angles Converse

Edplanation:

13 ~= 12

13 altenated angle to nr.10

13 is parpendicular to nr.15 and 15 is alternate to 12

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

area of equilateral triangle =

[tex]( \sqrt{3 } \div 4) \times a {}^{2} [/tex]

(C) area = 84.9 in²

The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing quadratically?


x f(x) g(x)
1 3 3
2 6 9
3 11 27
4 18 81
5 27 243
f(x), because it grows faster than g(x)
g(x), because it will not intersect f(x)
g(x), because it grows slower than f(x)
f(x), because it grows slower than g(x)

Answers

f(x) is the quadratic function.  

g(x) is tripling its output for each 1-unit increase in x and g(x) = 3^x.

A quadratic function always grows more slowly than an exponential function.

So the best answer is:
f(x), because it grows slower than g(x)

A number cube is rolled 500 times. Here are the results: Outcome Rolled 1 2 3 4 5 6 Calculate the following probabilities to the nearest thousandth. The theoretical probability of rolling a 5 or 6 The experimental probability of rolling a 5 or 6 [Choose ] Number of Rolls 81 95 79 89 80 76 [Choose]​

Answers

Answer:

The theoretical probability of rolling a 5 or 6 can be calculated by finding the sum of the probabilities of rolling a 5 and rolling a 6. Since the number cube has 6 equally likely outcomes, the probability of rolling a 5 or 6 is:

Theoretical probability = (probability of rolling a 5) + (probability of rolling a 6)

= 1/6 + 1/6

= 2/6

= 1/3

The experimental probability of rolling a 5 or 6 can be calculated by dividing the number of times a 5 or 6 was rolled by the total number of rolls. From the given data, the number of rolls for each outcome is:

Outcome | Number of Rolls

1 | 81

2 | 95

3 | 79

4 | 89

5 | 80

6 | 76

Experimental probability = (number of times a 5 or 6 was rolled) / (total number of rolls)

= (number of times a 5 was rolled + number of times a 6 was rolled) / 500

= (80 + 76) / 500

= 156 / 500

= 0.312

Therefore, the theoretical probability of rolling a 5 or 6 is 1/3, and the experimental probability is approximately 0.312.

Step-by-step explanation:

Will someone please answer this and show me how you got it

Answers

(a) Using Excel, the calculations are shown below:

Mean = 608.67

Median = 610.00

Mode = 610.00

Standard Deviation =  96.89

(b) The measure of central tendency would be appropriate are  the median and the mode.

How do we calculate?

The median is fitting  because it  is a representation of the middle value in the data set and is not affected by extreme values.

We can see that our  median rent is $610.00 and an appropriate representation of the typical rent paid by the students.

The mode is $610.00 and also an indication that this rent amount is the most common among the students.

In conclusion, a  measure of the variability or dispersion in the data set is provided by the standard deviation, which is determined to be 96.89. It demonstrates how widely the rents vary from the mean.

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Pizza General charges 10 dollars per medium pizza and a 5-dollar delivery fee. Fill in the table to show how much you would pay to get each number of pizzas delivered. Make sure to consider both the cost of the pizzas and the delivery fee.NOWWWWW

Answers

Answer:

Step-by-step explanation:

$15 for one pizza it's simple

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

The meaure of m∠KJL in the circle is:

m∠KJL = 25°

How to find the angle m∠KJL in the circle?

Since ΔJKL is inscribed in circle P with diameter JK and mJL = 130°. Thus, m∠JLK is an inscribed angle.

Since an angle inscribed in a semicircle is a right angle.

Thus, m∠DFE = 90°

Since the measure of inscribed angle is half the measure of its intercepted arc. Thus:

m∠JKL = 1/2 * mJL

m∠JKL = 1/2 * 130

m∠JKL = 65°

Therefore:

m∠KJL = 180 - 90 - 65 = 25° (sum of angles in a triangle)

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50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

Answer:

B. Similar

Step-by-step explanation:

The two spheres are similar, but not congruent. They have the same shape, but different sizes.

The scale factor between the two spheres is 9/6= 3/2, which means that the radius of the larger sphere is 3/2 times the radius of the smaller sphere.

Results:
1. Machine A costs the most but offers the highest increase in coffee output. Operating the machine can be difficult, so employees will need training.
2. Machine B costs $100 less than machine A, produces acceptable coffee output, and is simple to use. No training is required.
3. Machine C costs the least, produces slightly less than the current machine, and is simple to use. No training is required.
11
Select the correct answer from each drop-down menu.
Complete the sentence to tell why the writer has created this proposal.
The writer has written the proposal to
A) determine which kind of coffee most people like
B) compare different coffee makers before making a purchase
C) analyze the budget for buying a new coffee maker

Answers

Answer:

Step-by-step explanation:

imagine copy and pasting your question.

100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!

Answers

The value of x is,

⇒ x = 21.65

We have to given that,

A right triangle is shown in image.

Since, The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Hence, We get;

⇒ 25² = 12.5² + x²

⇒ 625 = 156.25 + x²

⇒ x² = 625 - 156.25

⇒ x² = 468.75

⇒ x = 21.65

Thus, The value of x is,

⇒ x = 21.65

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Please only answer if u actually know pls!

Answers

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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Find the equation using the point slope formula or slope intercept formula for the two sets of points. (19,-16) (-7,-15)

Answers

The equation of the Line passing through the points (19, -16) and (-7, -15) is: y = (-1/26)x - 397/26

The equation of a line using the point-slope formula or the slope-intercept form, we need either the slope of the line or the y-intercept. Let's calculate the slope of the line using the given points (19, -16) and (-7, -15).

The slope (m) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Using the coordinates (19, -16) as (x1, y1) and (-7, -15) as (x2, y2), we can substitute these values into the slope formula:

m = (-15 - (-16)) / (-7 - 19)

m = (-15 + 16) / (-7 - 19)

m = 1 / (-26)

m = -1/26

Now that we have the slope of the line, we can use either the point-slope formula or the slope-intercept form to find the equation.

Using the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope (-1/26) and one of the given points (19, -16) into the equation:

-16 = (-1/26) * 19 + b

To solve for b, we can simplify the equation:

-16 = -19/26 + b

To isolate b, we can add 19/26 to both sides of the equation:

-16 + 19/26 = b

Now, we can find the common denominator of 26 and add the fractions:

(-416 + 19) / 26 = b

-397/26 = b

Therefore, the equation of the line passing through the points (19, -16) and (-7, -15) is: y = (-1/26)x - 397/26

This equation represents the line with a slope of -1/26 and a y-intercept of -397/26.

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What is 7385.35 multiplied by 527.35

Answers

3894664.323 is your answer

Multiplying polynomials 4n2(n2 + 5n - 8)

Answers

Answer:

4n^4 + 20n^3 - 32n^2

Step-by-step explanation:

We have to distribute 4n2 to each term.

4n2 x n2. We can multiply the two n2 together resulting in 4n^4.

Now we do 4n2 x 5n. Here we multiply 4 x 5 which equals 20. Then, we multiply the n2 and n. Which results in n^3. Now we put them together; 20n^3.

Finally, we multiply 4n2 by -8. Since 8 doesn't have any variables, we just multiply the 4 and -8. Which equals to -32, now we just combine -32 and the variable; -32n2.

Now we combine these terms together. Our final answer is, 4n^4 + 20n^3 -32n^2.

^ represents an exponent.

I'll mark whoever answers first!! Please help me

Answers

Answer:

Center ( -8, 1 )

Radius ( 13 )

This figure represents the net of a square pyramid.
2 m
76
6 m
2 m

Answers

The total surface area of the square pyramid is 28 m²

What is an equation?

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Given the square pyramid net:

Area of square base = 2 m * 2 m = 4 m²

Area of each triangle face = (1/2) * 2 m * 6 m = 6 m²

Area of the four triangle face = 4 * 6 m² = 24 m²

Total surface area = 24 m² + 4 m² = 28 m²

The total surface area is 28 m²

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Complete the proof that HJ LGI.
4
I
5
Statement
K
1
ZHKI ZGKH
2
m2GKH + mZHKI = 180°
3 m2GKH+mZGKH= 180°
mZGKH = 90°
HJ L GI
G
H
Reason
Given
Angles forming a linear pair sum to 180°
Definition of congruence
(

Answers

The complete sentence is shown below:

Reason: Given

Reason: Angles forming a linear pair sum to 180° (Given)

Reason: Substitution from Statement 1.

To complete the proof that HJ GI, we can use the given statements and reasons:

Statement 1: <HKI = <GKH

Reason: Given

Statement 2: m<GKH + m<HKI = 180°

Reason: Angles forming a linear pair sum to 180° (Given)

Statement 3: m,GKH + m<GKH = 180°

Reason: Substitution from Statement 1

Statement 4: m<GKH = 90°

Reason: From Statement 2 and Statement 3, we can subtract m<GKH from both sides, which results in m<GKH = 180° - m<GKH.

Since the angles forming a linear pair sum to 180°, m<GKH + m<GKH = 180° implies that m<GKH = 90°.

Therefore, based on the given statements and reasons, we can conclude that HJ and GI are congruent (m<GKH = 90°)

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Triglycerides are a type of fat in the bloodstream. The mean triglyceride level in the United States is 134 milligrams per deciliter. Assume the triglyceride levels of the population of the United States are normally distributed, with a standard deviation of 35 milligrams per deciliter. You randomly select a person from the United States. What is the probability that the person's triglyceride level is less than 80?

Answers

The probability that a aimlessly  named person's triglyceride  position is  lower than 80 milligrams per deciliter is  roughly0.0618 or6.18.    

 

To calculate the probability that a aimlessly  named person's triglyceride  position is  lower than 80 milligrams per deciliter, we can use the conception of standard normal distribution.  

First, we need to  regularize the value of 80 using the z- score formula  z = ( x- μ)/ σ  Where  x =  80( the value we want to calculate the probability for)  μ =  134( mean triglyceride  position)  σ =  35( standard  divagation)  Plugging in the values, we get  z = ( 80- 134)/ 35  z = -54/ 35  z ≈-1.543

Next, we need to find the corresponding area under the standard normal distribution  wind for a z- score of-1.543. We can use a standard normal distribution table or a calculator to find this area.

Looking up the z- score in the table or using a calculator, we find that the area to the left wing of z = -1.543 is  roughly0.0618.  

thus, the probability that a aimlessly  named person's triglyceride  position is  lower than 80 milligrams per deciliter is  roughly0.0618 or6.18.

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Which graph represents the solution set to the system of inequalities?

Y ≤ 2X+2
1/2X + Y <7
Y- 3 ≥ 0

ANSWER is Down Below

Answers

The solution set to the system of inequalities will be the overlapping region or the intersection of the shaded regions from all three inequalities.

The system of inequalities consists of three inequalities:

y ≤ 2x + 2

(1/2)x + y < 7

y - 3 ≥ 0

Let's analyze each inequality:

y ≤ 2x + 2 represents a shaded region below the line with a slope of 2 and a y-intercept of 2.

(1/2)x + y < 7 represents a shaded region below the line with a slope of -1/2 and a y-intercept of 7.

y - 3 ≥ 0 represents a shaded region above the line with a slope of 0 and a y-intercept of 3.

The solution set to the system of inequalities will be the overlapping region or the intersection of the shaded regions from all three inequalities.

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Use the given proof to answer the question below:
Given ABCD is a parallelogram.
Prove: ADCB
D
A
1
2
3
4
S
6
Statements
ABCD is a parallelogram
ABI CD and AD IBC
and
AC = AC
ADCA ABAC
AD CB
Which of the options below complete the proof?
A. Statement 3: LBACZCAD and ZBCA LDCA
Reason 5: A.A.S. Postulate
B. Statement 3: LBACCAD and ZBCA = LDCA
Reason 5: A.S.A Postulate
C. Statement 3: LBAC LDCA and LBCA LDAC
Reason 5: A.A.S. Postulate
D. Statement 3: ZBAC LDCA and LBCA LDAC
Reason 5: A.S.A Postulate
Reasons
Given
Definition of parallelogram
Alternate interior angles theorem
Reflexive property
C.P.C.T.C.

Answers

The correct option is D.

Given that ABCD is a parallelogram, we need to prove AD ≅ CB.

So,

Properties of a parallelogram =

Opposite sides are parallel.

Opposite sides are congruent.

Opposite angles are congruent.

             Statement                                                    Reason

1. ABCD is a parallelogram                                           Given

2. AB║CD and AD║BC                                      Definition of parallelogram

3. ∠BAC ≅ ∠DCA and ∠BCA ≅ ∠DAC    Alternate interior angles theorem

4. AC ≅ AC                                                              Reflexive property

5. ΔBAC ≅ ΔDCA                                                       A.S.A Postulate

6. AD ≅ CB                                                                        CPCTC

Hence the correct option is D.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

The length of PQ in circle R is given as follows:

C) 3.14 m.

What is the measure of the circumference of a circle?

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius for the circle in this problem is given as follows:

r = 3 m.

Hence the circumference for the entire circle is given as follows:

C = 2 x 3.14 x 3

C = 18.84 m.

The sector has an angle measure of 60º, while the entire circumference is of 360º. hence the measure of arc PQ is given as follows:

PQ = 60/360 x 18.84

PQ = 3.14 m.

Hence option C is the correct option in the context of this problem.

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What is the area of the rectangle above?
OA. 96 square units
OB. 20 square units
OC. 104 square units
OD. 40 square units

Answers

The area of the rectangle with a length of 12 units and a width of 8 units is 96 sqaure units.

How to determine the area of a rectangle?

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The area of a rectangle is expressed as;

Area = length × breadth

From the image:

Length of the rectangle = 12 units

Breadth of the rectangle = 8 units

Area of the rectangle = ?

Plug the given values into the above formula and solve for the area:

Area = length × breadth

Area = 12 units × 8 units

Area = 96 sqaure units

Therefore, the measure of the area is 96 sqaure units.

Option A) 96 sqaure units is the correct answer.

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(09.03 MC)
The daily temperature in the month of February in a certain country varies from a low of 28°F to a high of 50°F. The temperature reaches the
freezing point of 32°F when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that
would model this periodic phenomenon?
O a
Ob
Oc
Od
Amplitude 11°F; period - 8 hours; midline: y = 39
Amplitude 11°F; period=4 hours; midline: y = 11
Amplitude = 22°F; period - 8 hours; midline: y = 39
Amplitude = 22°F; period - 4 hours; midline: y = 11

Answers

Answer:

The correct answer is:

Amplitude = 11°F; period = 8 hours; midline: y = 39

Step-by-step explanation:

Answer: A

Step-by-step explanation: Amplitude 11°F; period - 8 hours; midline: y = 39

If 5sinA=3 and cosA is smaller than 0 , with an aid of a diagram determine the value of 2tanAcosA

Answers

If 5sinA=3 and cosA is smaller than 0  , the value of 2tanAcosA is -6/5.

To determine the value of 2tanAcosA, we need to find the values of tanA and cosA first. We are given that 5sinA = 3 and cosA is smaller than 0.

Let's start by finding sinA. Since sinA = opposite/hypotenuse, we can set up a right triangle with the opposite side as 3 and the hypotenuse as 5. Using the Pythagorean theorem, we can find the adjacent side:

adjacent^2 = hypotenuse^2 - opposite^2

adjacent^2 = 5^2 - 3^2

adjacent^2 = 25 - 9

adjacent^2 = 16

adjacent = 4

Now we can find cosA using the adjacent side and hypotenuse:

cosA = adjacent/hypotenuse

cosA = 4/5

Since cosA is smaller than 0, it means that cosA is negative. Therefore, cosA = -4/5.

Next, we can find tanA using the given information. tanA = opposite/adjacent = 3/4.

Now, we can calculate the value of 2tanAcosA:

2tanAcosA = 2 * (3/4) * (-4/5) = -24/20 = -6/5

Therefore, the value of 2tanAcosA is -6/5.

To aid in visualizing the situation, it would be helpful to draw a right triangle with the appropriate side lengths based on the given values of sinA and cosA. The opposite side would be 3, the adjacent side would be 4, and the hypotenuse would be 5. Additionally, since cosA is negative, we can indicate the direction of the adjacent side to be in the negative x-axis direction. This diagram would provide a visual representation of the values and relationships involved in solving the problem.

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What is the meaning of "we shall use in formulas other symbols, namely defined predicates, operations, and constants, and even use formulas informally"?

Answers

The statement indicates that in practical applications, it is common to extend the basic logical language with additional symbols and allow for some degree of informality in the representation of formulas, as long as it is clear that these additional symbols and formulas can be formalized in terms of the basic logical language.

What does the statement mean?

The statement means that when working with formulas in a particular context or domain, it is common to introduce additional symbols beyond the basic logical symbols such as "E" (for existential quantification) and "∧" (for conjunction). These additional symbols can include defined predicates, operations, and constants.

Defined predicates refer to predicates or relations that are defined in terms of other predicates or relations. They can be used to express complex concepts or conditions in a concise manner. For example, in mathematics, one may define a predicate "Prime(x)" to represent the concept of a number being prime.

Operations refer to functions or operations that can be applied to terms or formulas. They allow for combining or manipulating expressions in a meaningful way. For instance, addition, multiplication, and exponentiation are common operations in mathematics.

Constants are symbols that represent specific, fixed values. They can be used to denote specific objects or elements within the domain of discourse. For example, in logic, "0" and "1" can be used as constants to represent the truth values "false" and "true," respectively.

Furthermore, the statement suggests that formulas may be used informally, meaning that they can be expressed or written in a less strict or precise manner. While the informal representation of formulas may be easier to understand or work with, it is understood that each of these formulas can be translated or reformulated in a way that only involves the basic logical symbols (such as "E" and "∧") and the specified nonlogical symbols (such as defined predicates, operations, and constants).

Overall, the statement acknowledges that in practical applications, it is common to extend the basic logical language with additional symbols and allow for some degree of informality in the representation of formulas, as long as it is clear that these additional symbols and formulas can be formalized in terms of the basic logical language.

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the headlights on a car are set so the light beam drops 2 in. for 26 ft measured horizontally. If the headlights are mounted 24 in. above the ground, how far ahead of the car will they hit the ground?>

Answers

Answer:

0.168 ft aprox

Step-by-step explanation:

To solve this problem, we can use similar triangles and proportions. Let's denote the distance ahead of the car where the light beam hits the ground as "x" (in feet).

According to the given information, the light beam drops 2 inches for every 26 feet horizontally. We can set up the following proportion:

2 inches / 26 feet = x inches / x + 26 feet

To solve for x, we can cross-multiply and solve the resulting equation. Let's convert inches to feet to maintain consistent units:

2 inches = 2/12 feet = 1/6 feet

1/6 feet / 26 feet = x feet / x + 26 feet

1/6 * (x + 26) = 26 * x

x/6 + 26/6 = 26x

x + 26 = 156x

156x - x = 26

155x = 26

x = 26 / 155 ≈ 0.168 ft

Therefore, the headlights will hit the ground approximately 0.168 feet (or 2.016 inches) ahead of the car.

the following number of people attended last 10 screenings of a movie. mean median or mode

Answers

We can see here that the measure that should be used to summarize the data is: A. Mean.

What is mean?

The mean, which is used to indicate the average value of a group of values in statistics, is a measure of central tendency. It is determined by adding up all of the dataset's values and then dividing the total by the number of values.

Mean = (Sum of all values) / (Total number of values)

The mean is widely used in statistics to summarize and describe the average value of a dataset. It is a useful measure for understanding the central tendency of a set of values.

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The complete question is:

The following number of people attended last 10 screenings of a movie.

196, 197, 198, 199, 202, 203, 204, 205, 206, 208

Which measure should be used to summarize the data?

A. Mean

B. Median

C. Mode

PLEASE HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The distance across the stream is 198 m.

We have,

ΔABC and ΔEBD are similar.

This means,

Corresponding sides ratios are the same.

Now,

AC/ED = AB/BE

Substituting the values.

x/360 = 220/400

x = 220/400 x 360

x = 22/40 x 360

x = 22 x 9

x = 198

Thus,

The distance across the stream is 198 m.

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What is absolute value and how do you find the absolute value of a number?
Find the absolute value of the following numbers:
|17| |−25| |−1.23| |0.45|
Identify whether each of the following is rational or irrational: 234 5–√
Convert the decimal 0.44444… to a fraction.
Match the number on the left with its classification on the right. Number Classification 0.3333… nonrepeating decimal 3.48372… repeating decimal 3.3 terminating decimal

Answers

Absolute value is a mathematical function that gives the distance of a number from zero on the number line.

How to explain the information

Let's find the absolute value of the given numbers:

|17| = 17

|−25| = 25

|−1.23| = 1.23

|0.45| = 0.45

Now, let's identify whether the following numbers are rational or irrational:

234: This is a rational number because it can be expressed as a fraction (e.g., 234/1).

5–√: This is an irrational number because it cannot be expressed as a fraction or a ratio of integers. The square root of 5 is not a perfect square, so it is irrational.

To convert the decimal 0.44444... to a fraction, we can set it as the variable x and solve the equation:

x = 0.44444...

Multiply both sides by 10 to move the decimal point:

10x = 4.44444...

10x - x = 4.44444... - 0.44444...

9x = 4

Divide both sides by 9:

x = 4/9

Therefore, the decimal 0.44444... is equivalent to the fraction 4/9.

Matching the numbers with their classifications:

0.3333...: This is a repeating decimal.

3.48372...: This is a nonrepeating decimal.

3.3: This is a terminating decimal.

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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!

Answers

The missing angles are m ∠1 = 53° and m ∠k = 12°.

Given that are two circles we need to find the missing measures,

Using the concept of intersecting chords angles,

When two chords intersect inside a circle, the angle between the chords is half the sum of the intercepted arcs.

And,

When two chords intersect outside a circle, the angle between the chords is half the difference of the intercepted arcs.

So,

a) m ∠1 = 1/2 [arc LP + arc RQ]

m ∠1 = 1/2 [50°+56°]

m ∠1 = 1/2 × 106°

m ∠1 = 53°

b) m ∠k = 1/2 [arc MJ - arc LR]

arc LR = 360° - [72° + 100° + 140°]

arc LR = 48°

So,

m ∠k = 1/2 [72° - 48°]

m ∠k = 12°

Hence the missing angles are m ∠1 = 53° and m ∠k = 12°.

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