1.

In the figure,ray OS is in a line POQ .Ray OR and ray OT are angle bisector of angle POS and angle SOQ .If angle POS =X . Find angle ROT

Answer»

Given,
RAY OS stand on a LINE POQ
Ray OR bisector of angle POS
Ray OT bisector of angle SOQ
Angle POS=x

by linear PAIR
angle POS+angle SOQ=180°
x+angle SOQ=180°
Angle SOQ=180°-x

Ray OR bisector of angle POS-
Angle POR+Angle ROS= Angle POS
2anglePOR=Angle POS(Angle POR=Angle ROS)
2angle POR=x
angle POR=x/2

Ray OT bisector of angle SOQ
Angle SOT+Angle TOQ=angle SOQ
2angle SOT=180°-x(angle SOT=angle TOQ)
angle SOT=(180°-x)/2
=90°-x/2
angle ROS+angle SOT=angle ROT
x/2+90°-x/2=angle ROT
90°=angle ROT
ANSWER


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