In ∆PQR of Fig. 6.32, PQ = PR. Find the measures of ∠Q and ∠R.

Given: ∠P = 30° ; PQ = PR

Formula Used/Theory:-

If 2 sides of triangle are equal

Then it will isosceles triangle

And its base angle will also be equal

→ Angle sum property

Sum of all angles of triangle is 180°

In Δ PQR

As PQ = PR

Hence;

Δ PQR is isosceles triangle

∴ ∠Q = ∠R

By angle sum property

Sum of all angles of triangle is 180°

∠P + ∠Q + ∠R = 180°

30° + ∠Q + ∠Q = 180°

2∠Q = 180° - 30°

2∠Q = 150°

∠Q = = 75°

As ∠Q = ∠R

∠R = 75°

Result:- ∠Q = ∠R = 75°