Question

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.

Answer 1

Given : Ray OS stand on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and  ∠SOQ  respectively. If ∠POS = x

 

Since, Ray OS stand on a line POQ :  

∠POS + ∠SOQ = 180° (Linear pair)

x + ∠SOQ = 180°

∠SOQ = 180°  – x

OT is the bisector of ∠SOQ :  

2∠SOT = 180°  – x

∠SOT = 1/2(180°  – x)

∠SOT = 90°  – x/2

OR is the bisector of ∠POS :  

∠ROS = ½ ∠POS  

∠ROS = ½ x  

∠ROS = x/2

Now,

∠ROT = ∠ROS + ∠SOT

∠ROT = x/2 + 90°  – x/2

∠ROT = 90°

Hence, ∠ROT is 90°.

HOPE THIS ANSWER WILL HELP YOU…..

 

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