Exercise 9 Page 106

Let's begin by reviewing the definitions of different types of angle pairs.

Pairs of Angles
Type	Definition	Relation of Measures
Supplementary Angles	Together, they form a straight line.	Their measures add up to 180^(∘).
Vertical Angles	They lie on the opposite sides of the point of intersection of two lines.	They are always congruent.
Corresponding Angles	They lie in corresponding positions on the same side of the transversal.	They are congruent in the case of two parallel lines cut by a transversal.
Alternate Interior Angles	They lie between the two lines on opposite sides of the transversal.	They are congruent in the case of two parallel lines cut by a transversal.
Alternate Exterior Angles	They lie outside the two lines on opposite sides of the transversal.	They are congruent in the case of two parallel lines cut by a transversal.

Now, let's take a look at the given diagram. We will focus on the three lines. Lines m and n are parallel and line t is the transversal.

Next, we want to choose which angle measure does not belong with the other three.

Notice that ∠ 2 and ∠ 6 are corresponding angles and ∠ 2 and ∠ 8 are alternate exterior angles. Corresponding angles are congruent and alternate exterior angles are congruent when two parallel lines are cut by a transversal. This means that these three angles are congruent.

Therefore, the only angle measure that does not belong with the other three is the measure of ∠ 5.

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