Recall that if a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent. Therefore, ∠ 1 and the 80^(∘) angle are congruent. This means that their measures are equal.
m ∠ 1 = 80
By the same fact, we know that the measures of ∠ 2 and ∠ 3 are equal.
m ∠ 2 = m ∠ 3
Next, because the bases of trapezoids are parallel, we can say that the 80^(∘) angle and ∠ 3 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.
80+m ∠ 3 = 180 ⇔ m ∠ 3 = 100
We already know that m ∠ 2=m ∠ 3, so m ∠ 3 is also equal to 100. Let's add the measures of these angles to our diagram.
