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Question

In the figure, $$\angle PQR=\angle PRQ$$, then prove that $$\angle PQS=\angle PRT$$.
463644.jpg


Solution

As Given, $$\angle PQR = \angle PRQ$$

To prove: $$\angle PQS = \angle PRT$$

According to the question,

$$\angle PQR +\angle PQS = 180^{\circ}$$  $$\mid$$ Linear Pair

$$\Rightarrow \angle PQS = 180^{\circ} - \angle PQR $$--- (i)

Also $$\angle PRQ +\angle PRT = 180^{\circ}$$ $$\mid$$ Linear Pair

$$\Rightarrow PRT = 180^{\circ} - \angle PRQ$$

$$\Rightarrow \angle PRQ = 180^{\circ} - \angle PQR --- (ii)$$$$ (\angle PQR = \angle PRQ)$$

From (i) and (ii),

$$\angle PQS = \angle PRT = 180^{\circ} - \angle PQR$$

$$\therefore \angle PQS = \angle PRT$$    $$[hence \, proved]$$

Mathematics
RS Agarwal
Standard IX

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