Cumulative Practice
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Remember when alternate exterior angles are congruent.
40
We are given two parallel lines and a transversal, and we are asked to find the value of x.
The angle of measure x and the angle of measure 140 ^(∘) are exterior angles. Remember that, when a transversal intersects two parallel lines, the alternate exterior angles are congruent. Let's write the measures of the exterior angles that are congruent to 140 ^(∘) and to the angle of measure x.
Let's review what we know about different types of angle pairs. We will use the graph below as an example.
Now let's take a look at the different types of angle pairs and their definitions.
| Pairs of Angles | ||
|---|---|---|
| Type | Definition | Example |
| Supplementary Angles | Together, they form a straight line and their measures add up to 180^(∘). | ∠ 1 and ∠ 3 |
| Vertical Angles | They lie on the opposite sides of the point of intersection of two lines. | ∠ 1 and ∠ 4 |
| Corresponding Angles | They lie in corresponding positions on the same side of the transversal. | ∠ 3 and ∠ 7 |
| Alternate Interior Angles | They lie between the two lines on opposite sides of the transversal. | ∠ 4 and ∠ 5 |
| Alternate Exterior Angles | They lie outside the two lines on opposite sides of the transversal. | ∠ 2 and ∠ 7 |