We want to find the measure of ∠ R. We are given that TRAP ~ EZYD.
Since the triangles are similar, we know that the corresponding angles are congruent.
∠ P ≅ ∠ D
∠ A ≅ ∠ Y
∠ R ≅ ∠ Z
∠ T ≅ ∠ E
As we can see, ∠ R is congruent to ∠ Z. Therefore, their measures are equal.
m ∠ R= m ∠ Z
We need to find m ∠ Z before we can find m ∠ R.
Notice that ∠ D and ∠ E are a right angles. Therefore, m ∠ D = 90 and m ∠ E = 90. We also know the measure of ∠ Y. To find the measure of ∠ Z we can use the Polygon Angle Sum Theorem.
m ∠ Y + m ∠ D + m ∠ E + m ∠ Z = (n-2)180
Since our polygons are quadrilaterals, n=4. Let's substitute this value and the measures of the given angles into the above equation and solve for m ∠ Z.
