To find the measure of ∠ 5, we will first find m∠ 4. To do this, we will use the fact that corresponding angles between parallel lines are congruent. Since the angle with measure 43^(∘) and ∠ 4 are corresponding angles between parallel lines, they are congruent.
Congruent angles have the same measure, so the measure of ∠ 4 is 43^(∘). We can add this information to our diagram. Finally, note that ∠ 4 and ∠ 5 form a straight line.
These two angles are supplementary and therefore the sum of their measures is 180^(∘). With this information, we can finally find the measure of ∠ 5.
m∠ 5+43^(∘)=180^(∘)
⇕
m∠ 5=137^(∘)
