To find the measure of ∠ 7, we will use the fact that corresponding angles of parallel lines are congruent. Lines a and b are parallel and the given angle and ∠ 5 are corresponding angles, so these angles are congruent.
Congruent angles have the same measure, so the measure of ∠ 5 is also 140^(∘). Finally, note that ∠ 5 and ∠ 7 form a straight line.
This means that they are supplementary angles and the sum of their measures is 180^(∘). With this information, we can finally find the measure of ∠ 7.
m∠ 7+ 140^(∘)=180^(∘)
⇕
m∠ 7=40^(∘)
