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Linear Pair

In the figure...

Question

In the figure below, if $∠$ PQR = $∠$ PRQ, then, which of the following is/are true?

A

$∠$ PQR = $∠$ PQS

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B

$∠$ PRQ = $∠$ PRT

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C

$∠$ PQS = $∠$ PRT

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D

$∠$ QPR = $90^{\circ}$

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Solution

The correct option is C
$∠$ PQS = $∠$ PRT

$∠$ PQS + $∠$ PQR = $∠$ PRQ + $∠$ PRT (by linear pair)

But, it is given that, $∠$ PQR = $∠$ PRQ

Therefore, $∠$ PQS = $∠$ PRT

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In the figure below, if $∠$ PQR = $∠$ PRQ, then, which of the following is/are true?

Q. State True or False.

∠ P Q R = ∠ P R Q

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In below shown figure, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ. Then $Δ$ PQR is an isosceles Triangle.

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