Question

please answer these quesion please its very urgent

Answer 1

Hi friend!

Given,

PQ is a line
Ray OR is perpendicular to line PQ.
OS is another ray lying between rays OP and OR.
Need to prove : ∠ROS = ½ (∠QOS - ∠POS)

∠QOR = ∠POR = 90°

» ∠POS + ∠ROS = ∠POR
∠POS + ∠ROS = 90°
∠POS = 90° - ∠ROS ------(1)

» ∠QOS - ∠ROS = ∠QOR
∠QOS - ∠ROS = 90°
∠QOS = 90° + ∠ROS --------(2)

(2)-(1)

∠QOS - ∠POS = 90° + ∠ROS - (90° - ∠ROS)
∠QOS - ∠POS = 90° + ∠ROS - 90° + ∠ROS
∠QOS - ∠POS = 2∠ROS
2∠ROS = ∠QOS - ∠POS
∠ROS = ½(∠QOS - ∠POS)


Hence proved!

Hope it helps…