In Fig. 6.15, $ \angle \mathrm{PQR}=\angle \mathrm{PRQ} $, then prove that $ \angle \mathrm{PQS}=\angle \mathrm{PRT} $
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Given:

$\angle PQR=\angle PRQ$.

To do:

We have to prove that $\angle PQS=\angle PRT$.

Solution:

$SQRT$ is a line.

We know that,

The sum of the measures of the angles in linear pairs is always $180^o$.

$\angle PQS+\angle PQR=180^o$   (as they are linear pairs)

$\angle PRT+\angle PRQ=180^o$   (as they are linear pairs)

Therefore,

$\angle PQR=180^o-\angle PQS$..(i)

$\angle PRQ=180^o-\angle PRT$....(ii)

Since, 

$\angle PQR=\angle PRQ$

We get, by equating

$180^o-\angle PQS=180^o-\angle PRT$

This implies,

$\angle PQS=\angle PRT$.

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Updated on: 10-Oct-2022

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