Question

ray op bisects angle aob and oq is the Ray opposite to OP show that angle qob=angle qoa​

Answer 1

Answer:

ANGLE QOB + BOP = 180 [LINEAR PAIR]

ANGLE QOA + AOP = 180 [LINEAR PAIR]

BUT, AOP = BOP

THEREFORE QOB = 180 - BOP = 180 - AOP

AND, QOA = 180 - AOP

SO, QOA = QOB

HENCE PROVED

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Answer 2

Given: Ray OP bisects ∠ AOB and OQ is the ray opposite to OP.

To Find:  Show that  ∠ QOB= ∠ QOA.​

Solution:

Ray OP bisects ∠ AOB and OQ is the ray opposite to OP.

=> QOP is a straight line

also Ray OP bisects ∠ AOB

=>m ∠AOP = m∠BOP

QOP is a straight line

=> m∠QOA + m∠AOP = 180°

QOP is a straight line

m∠QOB + m∠BOP = 180°

Hence m∠QOB + m∠BOP  = m∠QOA + m∠AOP

m ∠AOP = m∠BOP  hence cancelling from both sides

=> m∠QOB = m∠QOA

=> ∠QOB ≅ ∠QOA

QED

Hence proved

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