Question

POQ is a line. ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ ROS= 1/2(∠ QOS-∠ POS)

Answer 1

Step-by-step explanation:

angleROS=1/2angleQOS-anglePOS

hence proved.......

Answer 2

Solution:

In the question, it is given that (OR ⊥ PQ) and POQ = 180°

So, POS+ROS+ROQ = 180°

Now, POS+ROS = 180°- 90° (Since POR = ROQ = 90°)

∴ POS + ROS = 90°

Now, QOS = ROQ+ROS

It is given that ROQ = 90°,

∴ QOS = 90° +ROS

Or, QOS – ROS = 90°

As POS + ROS = 90° and QOS – ROS = 90°, we get

POS + ROS = QOS – ROS

2 ROS + POS = QOS

Or, ROS = ½ (QOS – POS)

(Hence proved).