In the given figure lines AB and CD intersect
ato. If angle AOC + angle BOE = 70 and angle DOB
=40°, find angle BOE and reflex angle EOC.
​

Answer:

reflex angle EOC = 250°

Step-by-step explanation:

reflex angle EOC

= angle COA + angle DOA + angle DOB + angle BOE

angle DOB = 40° (given)

angle DOB + angle DOA = 180° (linear pair)

angle DOA = 180° - 40°

angle DOA = 140°

angle COA + angle DOA = 180° (linear pair)

angle COA = 180° - 140°

angle COA = 40°

angle COA + angle BOE = 70° (given)

angle BOE = 70° - 40°

angle BOE = 30°

Now,

we have,

reflex angle EOC = 40° + 140° + 40° + 30°

= 250°

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The proof that UX ≅ SV is shown.

Given: △STU an equilateral triangle

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Prove: UX ≅ SV

Triangle T X V is shown. Point S is on side T X and point U is on side T V. A line is drawn from points S to U to form equilateral triangle T S U. Lines are drawn from point S to point V and from point U to point X and intersect at point W.

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Statement
Reason
1. ∠TXU ≅ ∠TVS 1. given
2. ∠STV ≅ ∠UTX 2. reflex. prop.
3. △STU is an equilateral triangle 3. given
4. ST ≅ UT 4. sides of an equilat. △ are ≅
5. ? 5. AAS
6. UX ≅ SV 6. CPCTC
△SXU ≅ △TVS
△UVX ≅ △SXV
△SWX ≅ △UWV
△TUX ≅ △TSV
Mark this and return

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