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.

Answer 1

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°