Recall that if a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent. Therefore, ∠3 and the 45^(∘) angle are congruent. This means that their measures are equal.
m ∠3 = 45
By the same fact, we know that the measures of ∠1 and ∠2 are equal.
m ∠1 = m ∠2
Next, because the bases of trapezoids are parallel, we can say that the 45^(∘) angle and ∠1 are same-side interior angles. Angles that form same-side interior angles along one leg are supplementary. This means that they add up to 180.
45+m ∠1 = 180 ⇔ m ∠1 = 135
We already know that m ∠1=m ∠2, so m ∠2 is also equal to 135. Let's add the measures of these angles to our diagram.
