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What types of angle pairs do you know in case of two parallel lines cut by a transversal?
See solution.
Let's take a look at the given diagram of two parallel lines cut by a transversal.
We are asked to describe two ways in which we can find the measure of ∠ 5. Before we do that, let's review the definitions of different types of angle pairs.
| Pairs of Angles | |
|---|---|
| Type | Definition |
| Supplementary Angles | Together, they form a straight line and their measures add up to 180^(∘). |
| Vertical Angles | They lie on the opposite sides of the point of intersection of two lines. |
| Corresponding Angles | They lie in corresponding positions on the same side of the transversal. |
| Alternate Interior Angles | They lie between the two lines on opposite sides of the transversal. |
| Alternate Exterior Angles | They lie outside the two lines on opposite sides of the transversal. |
Now let's describe the different ways to find the measure of ∠ 5.
First, we can see that angle 65^(∘) and ∠ 1 together form a straight line. Therefore these angles are supplementary angles.
The measures of supplementary angles add up to 180^(∘). We can use this fact to find the measure of ∠ 1. ∠ 1+ 65^(∘)=180^(∘) ⇕ ∠ 1 = 115^(∘) Next, let's notice that ∠ 1 and ∠ 5 are corresponding angles because they lie in corresponding positions on the same side of the transversal. This means that they have the same measures. ∠ 5 = ∠ 1 = 115^(∘) The measure of ∠ 5 is 115^(∘).
Let's think of another way of finding the measure of ∠ 5. First, we can see that angle 65^(∘) and ∠ 6 are corresponding angles.
