Q. 1155.0( 1 Vote )
In ∆PQR of Fig. 6.32, PQ = PR. Find the measures of ∠Q and ∠R.
Answer :
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°
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