Question

P,Q,R,S,T are points on a circle with centre O so that $\angle$PTQ= 2 x $\angle$RTS and PQ is parallel to RS. If P,O,Q are in a straight line, then the value of $\angle$SOQ is ___.

Answer 1

$\angle$PTQ= 90 (angle in a semi circle)

Hence $\angle$RTS = 45.

$\angle$ROS = 90 ( Inscribed angle= 2 $\times$Angle at circumference)

OR=OS=OR (radius)

$\angle$RSO = $\angle$SOQ= 45${}^{\circ }$ (interior alternate angles)