Question

congruent figures and corresponding parts review △abc≅△xyz. find m∠a. because the triangles are congruent, all corresponding parts are congruent. use the order of the letters in the congruence statement to determine the corresponding parts. for example, ∠a≅∠x because a and x are each listed first. step 1 write out the congruence statements for the corresponding parts. sides: (overline{ab}congoverline{xy}), (overline{bc}congoverline{yz}), (overline{ac}congoverline{xz}) angles: ∠a≅∠x, ∠b≅∠y, ∠c≅∠z because ∠b≅∠y, m∠b = . step 2 use the triangle angle - sum theorem to find m∠a. m∠a + m∠b + m∠c = 180° ← triangle angle - sum theorem m∠a + 37+ = 180° ← substitute the known values. m∠a + 100 = 180° ← simplify. m∠a =

Explanation:

Step1: Determine the measure of ∠B

Since ∠B≅∠Y and m∠Y = 37°, then m∠B=37°.

Step2: Determine the measure of ∠C

Since ∠C≅∠Z and m∠Z = 63°, then m∠C = 63°.

Step3: Calculate m∠A using the Triangle Angle - Sum Theorem

We know that m∠A+m∠B+m∠C = 180°. Substitute m∠B = 37° and m∠C = 63° into the equation:
m∠A+37 + 63=180
m∠A+100 = 180
Subtract 100 from both sides:
m∠A=180 - 100
m∠A = 80°

Answer:

80