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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 ÐPOS and ÐSOQ respectively
`∠`POS = x
`∠`POS and `∠`QOS is linear pair
ÐPOS + ÐQOS = 180°
x + ÐQOS = 180°
`∠`QOS = 180 - x
Now, ray or bisector `∠`POS
∴ `∠`ROS = `1/2` `∠`POS
= `1/2`× x [ ∵ `∠`POS = x]
`∠`ROS = x
Similarly ray OT bisector `∠`QOS
∵`∠`TOS = `1/2` `∠`QOS
= `180/2` - x [∵ `∠`QOS = 180 - x]
=` 90/2` - x
∴ `∠`ROT = `∠`ROS + `∠`ROT
= `x/2`+ 90 -`x/2`
= 90°
∴`∠`ROT = 90°
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