Question:
In below fig, ray OS stand on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ respectively. If ∠POS = x, find ∠ROT?
Solution:
Given,
Ray OS stand on a line POQ
Ray OR and Ray OT are angle bisectors of ∠POS and ∠SOQ respectively
∠POS = x
∠POS and ∠SOQ is linear pair
∠POS + ∠QOS = 180°
x + QOS = 180
QOS = 180 - x
Now, ray or bisector POS
∠ROS = 1/2 ∠POS
x/2
ROS = x/2 [Since POS = x]
Similarly ray OT bisector QOS
∠TOS = 1/2 ∠QOS
= (180 - x)/2 [QOS = 180 - x]
= 90 - x/2
Hence, ∠ROT = ∠ROS + ∠ROT
= x/2 + 90 - x/2
= 90
∠ROT = 180°