Question

Given △PQR ≅ △STU, m∠R = 80°, and m∠S = 70°, what is the measure of ∠Q?

a) 30°
b) 40°
c) 50°
d) 60°

Answer 1

Given △PQR ≅ △STU, m∠R = 80°, and m∠S = 70°, The corresponding angle is 40° , The correct answer is option b) 40°

Step-by-step explanation:

Corresponding angles are a pair of angles formed when a transversal intersects two parallel lines. These angles occupy the same relative positions at each intersection point on the parallel lines. Specifically, if a transversal cuts through parallel lines, the angles in the same position at each intersection are called corresponding angles. Corresponding angles are congruent, meaning they have equal measures. This geometric concept is fundamental in understanding the relationships between angles formed by parallel lines and transversals. It plays a crucial role in solving problems involving angles and parallel lines in geometry.

If triangles △PQR and △STU are congruent, the corresponding angles are equal.

Given:

m∠R=80∘

m∠S=70 ∘

Then, m∠Q is the corresponding angle to m∠R in △PQR.

So, m∠Q=80∘

Therefore, the correct answer is:

b) 40°