Question

In ΔJKL ≅ ΔQRS. What is m∠Q? (Given: m∠J = 37 degrees, m∠K = 105 degrees)

A) 37 degrees
B) 105 degrees
C) 53 degrees
D) 73 degrees

Answer 1

In congruent triangles ∆JKL and ∆QRS, the measure of angle Q is equal to the measure of its corresponding angle J. Since m∠J is 37 degrees, m∠Q is also 37 degrees.

Step-by-step explanation:

The question provides information about two congruent triangles, ∆JKL and ∆QRS, and requires the measure of angle Q. Given that m∠J is 37 degrees and m∠K is 105 degrees in a congruent triangle, we first determine the measure of angle L using the fact that the sum of interior angles in a triangle is always 180 degrees. With angle J and K known, we calculate m∠L as 180 degrees − (37 degrees + 105 degrees) = 38 degrees.

Since triangles JKL and QRS are congruent, their corresponding angles are equal. Therefore, m∠Q will be congruent to m∠J. So, the measure of angle Q, m∠Q, is 37 degrees.