We want to find the measure of each numbered angle.
Let's focus on triangles â–³ XYZ and â–³ XZW separately.
Finding m∠1 and m∠2
We will investigate â–³ 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.
