Question

In the figure, , and both lines are intersected by transversal t. Complete the statements to prove that m∠1 = m∠5. (given) m∠1 + m∠3 = 180° (Linear Pair Theorem) m∠5 + m∠6 = 180° (Linear Pair Theorem) m∠1 + m∠3 = ∠5 + ∠6 ( ) m∠3 = m∠6 ( ) m∠1 = m∠5 (Subtraction Property of Equality)

Answer 1

Angle 3 is congruent to angle 6 because they are vertical angles (Vertical Angle Theorem).

Therefore, we can substitute m∠6 for m∠3 in the third statement.

m∠1 + m∠3 = ∠5 + ∠6 can be rewritten as m∠1 + m∠6 = ∠5 + m∠6.

Using the subtraction property of equality, we can simplify this to m∠1 = ∠5 + m∠6 - m∠6.

Simplifying further, we get m∠1 = m∠5. Therefore, we have proven that m∠1 is equal to m∠5.

Explanation:

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