We are given the following statement about the measures of some angles in the diagram.
If the measure of angle ∠ 2=58^(∘), then the measure of ∠ 5= .
When a transversal intersects parallel lines, the alternate interior angles are congruent. Alternate interior angles are the angles that lie on the inside of the parallel lines and on opposite sides of a transversal. In this case, lines r and s are parallel lines which are cut by the transversal t. Let's take a look at the given diagram.
We can see that ∠ 2 and ∠ 8 lie on the inside of the lines r and s and on opposite sides of the transversal t. This means they are alternate interior angles, so they are congruent. Congruent angles are angles which have the same measure, so the measure of ∠ 8 is the same as the measure of ∠ 2.
∠ 8=∠ 2=58^(∘)
Next, notice that ∠ 8 and ∠ 5 form a straight line.
Therefore, they are supplementary and the sum of their measures is 180^(∘) . With this information, we can find the measure of ∠ 5.
