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.
