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°?
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. 

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