Question

In Fig. 6.10, ray OS stands on a line POQ. Ray OR and ray OT are
angle bisectors of angle POS and anglr SOQ, respectively. If angle POS = x, find angle ROT.
​

Answer 1

Answer:

given

anglePOS=x

OR bisects anglePOS

angleROP=angleROS=1/2(anglePOS)

angleROP=angleROS=x/2

anglePOS+angleSOQ=180°

x+angleSOQ=180°

angleSOQ=180°-x

Answer 2

Solution:

Ray OS stands on the line POQ.

therefore,

∠POS + ∠SOQ = 180°

But,

∠POS = x

Therefore,

x + ∠SOQ = 180°

So,

∠SOQ = 180° - x

Now, ray OR bisects ∠POS, therefore,

∠ROS = 1/2 × ∠POS

= 1/2 × x = x/2

∠SOT = 1/2 × ∠SOQ

= 1/2 × (180°-x)

= 90° - x/2

Now,

∠ROT = ∠ROS + ∠SOT

= x/2 + 90° - x/2

= 90°