Question

nq and mp intersect at point o. neil noticed that: m∠1 = 180° - m∠2 m∠3 = 180° - m∠2 what theorem can neil prove using these equations? choose 1 answer: a vertical angles are congruent. b linear pair angles are complementary. c vertical angles are supplementary. d linear pair angles are congruent.

Explanation:

Since \(m\angle1 = 180^{\circ}-m\angle2\) and \(m\angle3 = 180^{\circ}-m\angle2\), we can set \(m\angle1=m\angle3\) by the transitive property. \(\angle1\) and \(\angle3\) are vertical - angles. Vertical angles are formed when two lines intersect. The fact that we can show \(\angle1\) and \(\angle3\) have equal measures proves that vertical angles are congruent.

Answer:

A. Vertical angles are congruent.