We want to find the measure of each numbered angle.
Let's focus on triangles △ XYZ and △ XZW separately.
Finding m∠ 1 and m∠ 2
We will investigate △ XYZ first.
The markers at ∠ 1 and ∠ 2 indicate that these are congruent angles, so they have the same measure.
m∠ 1=m∠ 2
We can use the given angle measure at X and the Triangle Angle-Sum Theorem to set up and solve an equation for m∠ 1. Recall that by this theorem, the sum of the measures of the three angles in a triangle is 180^(∘).
Since angles ∠ 1 and ∠ 2 are congruent, ∠ 2 has the same measure.
m∠ 1=m∠ 2=37.5^(∘)
Finding m∠ 3
To find the measure of ∠ 3, let's shift our focus to triangle △ XZW. In this triangle, the measure of two angles are given and we are asked to find the measure of the third angle.
We can use the Triangle Angle-Sum Theorem again for △ XZW to set up and solve an equation for m∠ 3.
