Question

In given figure, Angle PQR = Angle PRQ, then prove that Angle PQS = Angle PRT.​

Answer 1

$\huge\underline\mathfrak\purple{Solution}$

$SQR \: is \: a \: straight \: line \\ \angle \: y \: + \angle \: z = 180......(1) \: \: \: \: \: \: \: \: \: \: (Linear \: pair) \\ \\ TRQ \: is \: a \: straight \: line \\ \angle \: x \: + \angle \: z \: = 180......(2) \: \: \: \: \: \: \: \: \: (Linear \: pair) \\ \\ so \: ..(1) = \: ..(2) \\ \angle \: y \: + \angle \: z = \angle \: x \: + \angle \: z \\ \: \: \: \: \: \: \: \: \: \: \: \: \angle \: y \: = \angle \: z \\ Hence, \: \angle \: PQR \: = \angle \: PRT \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Hence \: proved$

HOPE it helps to you!!☺

Answer 2

Step-by-step explanation:

As angle PQS = angle PRT

Let us consider angle PQS = angle PRT = x

Let angle QPR = y

We know that, the sum of two interior angle is equal to the opposite exterior angle.

From this, we can say that

Angle PRQ + Angle QPR = angle PQS

=> x+y = angle PQS ....(i)

angle PQR + angle QPR = Angle PRT

=> x+y = angle PRT ....(ii)

From (i) & (ii), we can conclude that

angle PQS = angle PRT