Question

5. In the adjoining figure, POR is a straight line and OS is common ray
to both angles ZPOS and ZROS. Find the value of x, if
ZPOS = (5x +28) and ZROS = (4x – 10). Also find ZPOS and
ZROS.​

Answer 1

Step-by-step explanation:

It is given that OR is perpendicular to PQ

So that ∠POR = 90°

sum of angle in linear pair always equal to 180°

∠POS + ∠SOR + ∠POR = 180°

Plug ∠POR = 90°

90°+∠SOR + ∠POR = 180°

∠SOR + ∠POR = 90°

∠ROS = 90° − ∠POS … (1)

∠QOR = 90°

Given that OS is another ray lying between rays

OP and OR so that

∠QOS − ∠ROS = 90°

∠ROS = ∠QOS − 90° … (2)

On adding equations (1) and (2), we obtain

2 ∠ROS = ∠QOS − ∠POS

∠ROS = 1/2(∠QOS − ∠POS)

hope it helps