Question

POQ is a straight line. RO perpendicular to PQ and SO is a ray from O then prove that ROS = 1/2(QOS -POS)

Answer 1

∠ ROS = 1/2( ∠ QOS - ∠ POS) (Proved)

Step-by-step explanation:

See the attached diagram.

Now, let us assume that ∠ SOR = x°

So, ∠ QOS = x + 90 .......... (1)

and, ∠ POS = 90 - x ........... (2)

Now, from equations (1) and (2) we get,

∠ QOS - ∠ POS = (x + 90) - (90 - x) = 2x

⇒ x = ∠ ROS = 1/2( ∠ QOS - ∠ POS) (Proved)