Question

Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS= 1/2(∠QOS-∠POS). In Fig. 6.17, POQ is a line.

Answer 1

let the anglePOS=x and angleSOR=Y
x+y+90°=180°
y=90-x

angleROS let is y
angleROS=1/2(y+90°-(90°-y)
y = 1/2(y+90-90+y)
y=y
RHS=LHS

Answer 2

Answer:

∠ROS= 1/2(∠QOS-∠POS) .... Proved

Step-by-step explanation:

See the given diagram first.

From the given diagram we can write,

∠QOS= ∠QOR +∠ROS= 90°+ ∠ROS ......(1){Since it is given that OR is perpendicular on PQ line. Hence, ∠QOR=90°}

Now, ∠POS =∠POR- ∠ROS =90° -∠ROS ........ (2)){Since it is given that OR is perpendicular on PQ line. Hence, ∠POR=90°}

Now, subtracting equation (1) from equation (2), we get,  

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

⇒ ∠ROS= 1/2(∠QOS-∠POS) (Proved)