Can you think of a relationship between ∠ 4 and ∠ 6?
96^(∘), see solution.
Practice makes perfect
We want to find the measure of ∠ 6. Let's take a look at the photo of a portion of an airport.
Note that ∠ 3 and ∠ 4 form a straight line which means that they are supplementary angles. Therefore, their measures add up to 180^(∘).
∠ 3 +∠ 4=180^(∘)
We know that the measure of ∠ 4 is 84^(∘). We can use this fact to find the measure of ∠ 3. Let's substitute 84^(∘) for ∠ 4 in our equation.
Next, notice that ∠ 3 and ∠ 6 lie outside lines a and b on opposite sides of the transversal, so they are alternate exterior angles. Because lines a and b are parallel, ∠ 3 and ∠ 6 are congruent. This means that the measure of ∠ 6 is 96^(∘).
Extra
Types of Angle Pairs
There are different types of angle pairs. We will describe them using the example graph of two lines intersected by a transversal.
Now we will list all of the types of angle pairs together with their definitions and corresponding examples.
Pairs of Angles
Type
Definition
Example
Supplementary Angles
Together, they form a straight line and their measures add up to 180^(∘).
