PLEASE HELP!! 7. Marcy and Jake both explained why the following statement is true:
If mZABC +mZXYZ = 180' and ZABC - ZXYZ , then ZABC and ZXYZ are right angles.
Marcy's reasoning:
Since we are given that mZABC +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 2ABC & ZXYZ we can say that m ZABC = m_XYZ because congruent angles have equal
measures. This means that you can substitute m ZABC for m Zxyz in the equation
m_ABC +mZXYZ = 180°. We then have mZABC + m2ABC = 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?
Only Marcy is correct.
only Jake is correct.
Both Marcy and Jake are correct.
ONeither Marcy nor Jake is correct