Question

if angle POQ=72,PO is produced to any point R, XO bisects angle ROQ. Find the measure of reflex angle XOP​

Answer 1

answer: 234

expl:

POQ =72

POR= 180

ROQ=180-72=108

XO BISECTS ROQ. HENCE,

XOQ=ROX= 54

NOW,

REFLEX ANGLE XOP= 360 - XOQ - QOP

OR, REFLEX ANGLE XOP= 360-54-72 = 234

Answer 2

The measure of reflex angle ∠XOP is 234°

Given:

∠POQ = 72°

PO extended to R

XO bisects ∠XOP

To Find:

Reflex angle ∠XOP

Solution:

First, we have to calculate the ∠ROQ

∠POQ and ∠ROQ are in linear pairs, therefore we can apply the linear pair property here.

∴ ∠POQ + ∠ROQ = 180°

⇒ 72° + ∠ROQ = 180°

⇒ ∠ROQ = 180° - 72°

⇒ ∠ROQ = 108°

Now, since XO bisects ∠ROQ

∴ ∠XOQ = ∠ROQ / 2

⇒ ∠XOQ = 108° / 2

⇒ ∠XOQ = 54°

To find ∠XOP,

⇒ ∠POQ + ∠XOQ

⇒ 72° + 54°

⇒ 126°

Now, the measure of reflex angle ∠XOP,

⇒ 360° - ∠XOP

⇒ 360° - 126°

⇒ 234°        (Ans.)

Therefore, the measure of reflex angle ∠XOP is 234°

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