Question

Q21. In the given figure, POQ is a line. Ray OR is perpendicular to the line PQ. Os is another ray lying
between rays OP and OR. Prove that:
1
angle ROS=1/2 (angleQOS - angle POS)​

Answer 1

Answer:

From the figure

∠ROS+90

∘

=∠QOS⟹90

∘

=∠QOS−∠ROS

∠QOS+∠POS=180

∘

=2(90

∘

)

∠QOS+∠POS=2∠QOS−2∠ROS

⟹2∠ROS=∠QOS−∠POS

⟹∠ROS=

2

1

(∠QOS−∠POS)