Question

Marcy and Jake both explained why the following statement is true: If m/ABC +m/XYZ = 180° and ZABC = ZXYZ, then ZABC and ZXYZ are right angles. Marcy's reasoning: Since we are given that mABC +mZXYZ = 180°, we know that the measures of the two angles add up to 180°, and therefore the measure of each of the angles has to be half of 180°. Half of 180° is 90°. Since the measures of the angles are equal, they both measure 90°. This means that they are both right angles, since all right angles measure 90°.

Jake's reasoning: Since ZABC XYZ we can say that m ZABC = m/XYZ because congruent angles have equal measures. This means that you can substitute LABC for mZXYZ in the equation mABC +m/XYZ = 180°. We then have m/ABC+m/ABC = 180°, which can be simplified to 2 (m/ABC) = 180°. When we divide both sides by 2 we get m/ABC= 90°. Since both of the angles have equal measures, they are both 90°, which means they are both right angles.

Whose reasoning is correct?

A. Only Marcy is correct
B. Only Jake is correct
C. Both Marcy and Jake are correct
D. Neither Marcy nor Jake is correct​

Answer 1

Both Marcy and Jake are correct in their reasoning.

Marcy's reasoning correctly identifies that if the sum of two angles is 180°, and they are equal in measure, then each angle must measure 90°, which is characteristic of right angles.

Jake's reasoning correctly uses the fact that congruent angles have equal measures, and he appropriately substitutes m(ZXYZ) with m(ZABC) in the equation. His algebraic manipulation also correctly leads to the conclusion that both angles measure 90°, which makes them right angles.

So, the correct answer is:

C. Both Marcy and Jake are correct.