Question

Write a complete two-column proof for the following information.

Given: m<1 = 62° and lines t and l intersect
Prove: M<4 = 62°

Answer 1

To prove that m<4 = 62°, use the Vertical Angles Theorem and the given information. Since m<1 = 62° and lines t and l intersect, the vertical angles formed are congruent, so m<4 = 62°.

Step-by-step explanation:

To prove that m<4 = 62°, we can use the Vertical Angles Theorem. This theorem states that when two lines intersect, the vertical angles formed are congruent. In this case, m<1 and m<4 are vertical angles. Since m<1 = 62°, we can conclude that m<4 = 62° as well.

Therefore, the proof can be constructed as follows:

StatementsReasons1. m<1 = 62° (Given)Given2. m<4 = m<1 (Vertical angles are congruent)Vertical Angles Theorem3. m<4 = 62° (Substitution from Step 2)Substitution