Triangles ABC and PQR are congruent with AB = PQ = 8, BC = QR = 10, and angle B = 35°. Find the value of angle P + angle C.

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Accepted Answer

Given that △ABC ≅ △PQR, corresponding sides and angles are equal. We have AB = PQ = 8, BC = QR = 10, and ∠B = 35°. Since the triangles are congruent, ∠B = ∠Q = 35°.

In triangle ABC, the sum of angles is 180°:
∠A + ∠B + ∠C = 180°
=> ∠A + 35° + ∠C = 180°
=> ∠A + ∠C = 145°

Similarly, in triangle PQR:
∠P + ∠Q + ∠R = 180°
=> ∠P + 35° + ∠R = 180°
=> ∠P + ∠R = 145°

Since the triangles are congruent, angles correspond as:
A ↔ P, B ↔ Q, C ↔ R

Therefore, ∠P + ∠C = ∠A + ∠C = 145°.

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