Question

If △ABC ≅ △PQR by SSS congruency and ∠A = 76°, then what is the ​sum of the measures of ∠Q and ∠R in △PQR?​

• A. 76°​
• B. 104°​
• C. 38°​
• D. 52°​

Answer 1

The correct option is B

104°​

In △ABC,
∠A = 76° (Given)
∠A + ∠B + ∠C = 180°
(Angle sum property of triangle)
⇒ ∠B + ∠C = 180° - 76° = 104°

It is given that, △ABC ≅ △PQR
So, ∠P = ∠A = 76° (by C.P.C.T.)

Now, in △PQR
∠P + ∠Q + ∠R = 180°
(Angle sum property of triangle)
⇒ ∠Q + ∠R = 180° - 76° = 104°