7. Marcy and Jake both explained why the following statement is true:
If mABC+mZXYZ = 180° and Marcy's reasoning:
Since we are given that mmABC+mXYZ = 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 LABC XYZ we can say that mABC = mAXYZ because congruent angles have equal
measures. This means that you can substitute ABC for m XYZ in the equation
m/ABC+m/XYZ = 180°. We then have mABC+mABC = 180°, which can be simplified to
2 (m/ABC)=180°. When we divide both sides by 2 we get 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?
Only Marcy is correct.
Only Jake is correct.
Both Marcy-and Jake are correct.
Neither Marcy nor Jake is correct