Exercise 33 Page 516

Let's start by examining the diagram in the book.

Note that ∠ 1 and ∠ 2 are consecutive interior angles. If we can show that these are supplementary, we can use the Consecutive Interior Angles Converse to prove that m and n are parallel lines. Let's first check the sum of the angles.

m∠ 1+m∠ 2

SubstituteII

m∠ 1= 115^(∘), m∠ 2= 65^(∘)

115^(∘)+ 65^(∘)

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Add terms

180^(∘)

Since ∠ 1 and ∠ 2 are supplementary angles, we have enough information to claim that m and n are parallel lines.

Let's also show this as a two-column proof.

Statement	Reason
1. m∠ 1 =115^(∘), m∠ 2 =65^(∘)	1. Given
2. m∠ 1+m∠ 2=m∠ 1+m∠ 2	2. Reflexive Property of Equality
3. m∠ 1+m∠ 2=115^(∘)+65^(∘)	3. Substitution Property of Equality
4. m∠ 1+m∠ 2=180^(∘)	4. Simplify
5. ∠ 1 and ∠ 2 are supplementary	5. Definition of supplementary angles
6. m∥ n	6. Consecutive Interior Angles Converse