In Fig. 8.46, ray OS stand on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠ respectively. If ∠POS = x, find ∠ROT.

Given that,

Ray OS stand on a line POQ

Ray OR and OT are angle bisector of ∠POS and ∠SOQ respectively.

∠POS = x

∠POS + ∠QOS = 180^o(Linear pair)

∠QOS = 180^o – x

∠ROS = ∠POS (Given)

= x

∠ROS =

Similarly,

∠TOS = (90^o - )

Therefore,

∠ROT = ∠ROS + ∠ROT

= + 90^o -

= 90^o

Therefore, ∠ROT = 90^o