Angle: m∠ 7=79^(∘) Theorems: Alternate Interior Angles Theorem and the definition of supplementary angles.
Practice makes perfect
It is given that m∠ 4=101^(∘). Let's use this information to find the measure of the angle ∠ 7. We will name the lines so that the explanations are easier. Angles ∠ 4 and ∠ 7 lie on opposite sides of the transversal t, but on the same bottom sides of the parallel lines n and m.
Let's find m∠ 7 in two steps. First, we can use the Alternate Interior Angles Theorem to find the measure of angle ∠ 6. From the previous exercise, we know that m∠ 6=101^(∘). Second, we can use the fact that ∠ 6 and ∠ 7 are supplementary angles and the sum of their measures is 180^(∘).
m∠ 6+m∠ 7=180^(∘)
If we substitute m∠ 6 with 101^(∘), we will be able to calculate m∠ 7.
101^(∘)+m∠ 7=180^(∘) ⇒
m∠ 7=180^(∘)-101^(∘)= 79^(∘)
Therefore, the measure of angle ∠ 7 is 79^(∘).
