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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

Respuesta :

W0lf93
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.
Yna9141
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. 

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