To find the measure of ∠ 3, we will first find m∠ 1. Recall that when two lines intersect, vertical angles are formed on opposite sides of the point of intersection, and these angles are always congruent.
Congruent angles have the same measure, so the measure of ∠ 1 is 80^(∘).
Now, note that ∠ 2 and the angles with measures 80^(∘) and 43^(∘) form a straight line.
Therefore, the sum of their measures is 180^(∘). With this information, we can find the measure of ∠ 2.
m∠ 2+43^(∘)+80^(∘)=180^(∘)
⇕
m∠ 2=57^(∘)
Let's add this information to our diagram.
Since ∠ 2 and ∠ 3 are corresponding angles between parallel lines, these angles are congruent. This means that they have the same measure.
m∠ 3 = m∠ 2
⇕
m∠ 3 = 57^(∘)
