1.

In Figure, ray `O S`stand on a line `P O Qdot`Ray `O R`and ray `O T`are angle bisectors of `/_P O S a n d /_S O Q`respectively. If `/_P O S=x ,`find `/_R O T`

Answer» `/_POS+/_SOQ=180^0-(1)`
`/_POS and /_SOQ` is linear pair of angles.
`/_POR=/_ROS
/_SOT+/_TOQ=/_SOQ`
`/_SOT=/_TOQ`
`x+/_SOQ=180^0`
`/_SOQ=180^0-x-(2)`
`2/_SOT=180^0-x`
`/_SOT=(180^0-x)/2`-(3)
`/_ROS=/_(POS)/2`
`/_ROS=x/2`
`/_ROT=/_SOT+/_ROS`
`(180-x)/2+x/2`
=`90^0`.


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