Question

In Fig. ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Answer 1

Data : In this figure, ∠PQR = ∠PRQ. 

To prove : ∠PQS = ∠PRT 

Proof : In ∆PQR, ∠Q = ∠R. 

∴ This is an isosceles triangle. 

Let ∠Q = 70°, then ∠R = 70° . 

∠PQS + ∠PQR = 180° 

∠PQS + 70° = 180° 

∴ ∠PQS =180 – 70 

∠PQS = 110° … (i) 

Similarly, ∠PRT + ∠PRQ = 180° 

∠PRT + 70° = 180° 

∴ ∠PRT = 180 – 70 

∠PRT =100 … (ii) 

from (i) and (ii) 

∠PQS = ∠PRT =110°, 

∴ ∠PQS = ∠PRS proved.