Question

In figure, sides QP and RQ of ∆PQR are produced to points S and T, respectively. If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.​

Answer 1

Given :-

A Triangle PQR , sides QP and RQ are produced to"S" and " T" respectively

Angle SPR = 135

Angle PQT = 110

Required:-

Angle PRQ

Solution:-

We have

Angle 1 + Angle SPR = 180 ( LINEAR PAIR)

Angle 1 + 135 = 180

Angle 1 = 180 - 135

Angle 1 = 45

BY EXTERIOR ANGLE THEROM,

Angle PQT = Angle 1 + Angle 2

= 110 = 45 + Angle 2

= 110 - 45 = Angle 2

= 65 = Angle 2

So Angle PRQ = 65

Note :-

Figure in attachment