Question

Line AB and PQ intersect at point O. If m∠AOP= 150°. Find the measure of ∠POB, ∠BOQ and ∠AOQ
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Answer 1

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Two lines AB and CD intersect each other at O

∠AOC = 68°

(i) ∵ AOB is a line

∠AOC + ∠BOC = 180°

⇒ 68° + a = 180°

⇒ a = 180°- 68° = 112°

(ii) ∠AOC and ∠BOD and ∠BOC and ∠AOD are the two pairs of vertically opposite angles .

(iii) ∠AOC and ∠BOC; ∠BOC and ∠BOD; ∠BOD and ∠DOA;

∠DOA and AOC are the pairs of adjacent angles

(iv) ∠BOC and ∠DOA are reflex angles and also ∠AOC and ∠BOD are also reflex angles

Ref. ∠BOC = 180° + 68° = 248°

Ref. ∠DOA = 180° + 68° = 248°

Ref. ∠AOC = 180° + 112° = 292°

and ref. ∠BOD =180° + 112° = 292°

Hope it will help you army

Good afternoon

Answer 2

Step-by-step explanation:

Two lines AB and CD intersect each other at O

∠AOC = 68°

(i) ∵ AOB is a line

∠AOC + ∠BOC = 180°

⇒ 68° + a = 180°

⇒ a = 180°- 68° = 112°

(ii) ∠AOC and ∠BOD and ∠BOC and ∠AOD are the two pairs of vertically opposite angles .

(iii) ∠AOC and ∠BOC; ∠BOC and ∠BOD; ∠BOD and ∠DOA;

∠DOA and AOC are the pairs of adjacent angles

(iv) ∠BOC and ∠DOA are reflex angles and also ∠AOC and ∠BOD are also reflex angles

Ref. ∠BOC = 180° + 68° = 248°

Ref. ∠DOA = 180° + 68° = 248°

Ref. ∠AOC = 180° + 112° = 292°

and ref. ∠BOD =180° + 112° = 292°

Hope it will help you army

Good afternoon