Let's put the measure of ∠2 on the diagram and focus on the angles at point N.
Angles ∠1 and ∠2 are vertical angles.
According to the Vertical Angles Theorem vertical angles are congruent, so they have the same measure.
Since we now know the measure of ∠2, this tells us the measure of ∠1.
m∠1=m∠2=59^(∘)
Finding m∠3
Let's put the measure of ∠1 on the diagram and switch our focus to triangle △ NPQ.
In this triangle we now know the measure of two angles and are asked to find the measure of the third angle.
We can use the Triangle Angle-Sum Theorem in triangle △ NPQ to set up and solve an equation for m∠3.
