Question

Ray OP bisects angle AOB and OQ is the opposite to OP. Show that angle QOB = angle QOA.

Answer 1

I. the bracket is reason

Answer 2

Answer:

Given:

OP bisects ∠AOB

OQ is opposite of OP

To prove- ∠QOB=∠QOA

Step-by-step explanation:

∠BOP=∠AOP

∵OP ray bisects ∠BOA. It divides it into two equal parts.

Now QP is a straight line,

∠BOQ+∠BOP=180°

∠QOA+∠AOP=180°

[The sum of all angles of a triangle is 180°]

Now,

∠QOB=180°-∠BOP

∠QOA=180°-∠AOP

Also,

∠QOA=180°-∠BOP [∵∠BOP=∠AOP]

Then,

∠QOB=∠QOA=180°-∠BOP

Therefore,

∠QOB=∠QOA

Hence proved.

#SPJ3