We want to find the value of c, which is the measure of the angle ∠ Z. We are given that TRSU ~ NMYZ.
Since the polygons are similar, we know that the corresponding angles are congruent.
∠ T ≅ ∠ N
As we can see, ∠ N is congruent to ∠ T. Therefore, their measures are equal.
m ∠ N= m ∠ T = 120
We know the measures of ∠ N, ∠ M, and ∠ Y. To find the measure of ∠ Z, we can use the Polygon Angle Sum Theorem.
m∠ N +m∠ M+m∠ Y+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.
