Two triangles, △ABC and △XYZ, are congruent. The measure of angle C, m∠C, is equal to 81°. The measure of angle X, m∠X, is equal to 56°. Select Yes or No.

A. Does m∠A = 99° Yes/No

B. Does m∠B = 43° Yes/No

C. Are m∠A and m∠Z congruent? Yes/No

A. Since we are given the congruence statement for the two triangles, we know that â A is congruent to â X. Both A and X appear first in the congruence statement. In like manner â B is congruent to â Y, and â C is congruent to â Z. We are also given that mâ X = 56°. When two angles are congruent, they have the same measurements. Therefore, â A also has a measurement of 56°. The answer to question A is NO, because â A does NOT measure 99°. Actually, mâ A = 56° B. In geometry we are given a theorem that states that the sum of the measurements of the angles in a triangle is always 180 degrees. To find the measurement of â C, we'll use the equation mâ A + mâ B + â C = 180°. Since we are given the measurements for two of the angles, we can replace them in the equation to get 56° + mâ B + 81° = 180°. We simplify to get 137° + mâ B = 180°. We subtract 137 from both sides to find that mâ B = 43°. So the answer to question B is YES. C. According to the congruence statement given us, â C and â Z are congruent. Also, we are given that mâ C = 81°, so mâ C = mâ Z = 81°. From question A we figured out that mâ A = 56°. Therefore, the answer to question C is NO because 81° and 56° are not the same, and the two angles are NOT congruent.

If the two polygons are congruent, the corresponding sides and corresponding angles should have the same measures.

(A) Does m∠A = 99°?

Answer: For ΔABC, we are given with the measure of ∠C as 81°. We are also given that measure of ∠X is 56°. This makes the measure of ∠A 56° because the corresponding angles are X and A. Thus, the answer to this item is NO.

(B) Does m∠B = 43°?

The measure of angle from (A) is 56° and the measure of ∠C is 81°. The sum of the measures of the angles in the triangle should be equal to 180°.

m∠B = 180 - 56 - 81 = 43°

Thus, this is true. Answer is YES.

(C) Are angle A and angle Z congruent?

The answer to this item is NO this is because the corresponding angle of A is X therefore it should be A and X that must be congruent.