Question

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In Fig. 8.48, 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).
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Answer 1

Answer:

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Answer 2

Answer:

Proved!

Step-by-step explanation:

Since QR ⊥ Q.

Hence,

$\angle \ rop \: = 90 \degree \: and \angle roq \: = 90 \degree$

We can say that,

$\angle \: rop \: = \angle \: roq$

So,

$\angle \: pos + \angle \: ros = \angle \: roq$

$\angle \: ros + \angle \: pos \: = \angle \: qos - \angle \: ros$

$\angle \: sor + \angle \: ros = \angle \: qos - \angle \: pos$

$2( \angle \: ros) = \angle \: qos - \angle \: pos$

$\angle \: ros\: = \dfrac{1}{2} ( \angle \: qos - \angle \: \: pos)$

Hence,

Proved...