Question

note: figure not drawn to scale.
triangle prs is similar to triangle xyz (not shown), where p corresponds to x and s corresponds to z. the perimeter of triangle xyz is 19 times the perimeter of triangle prs. what is the measure of angle z?
a $\frac{9}{19}^{circ}$
b $\frac{23}{19}^{circ}$
c $19^{circ}$
d $23^{circ}$

Explanation:

Step1: Recall the property of similar triangles

Similar triangles have equal corresponding angles.

Step2: Identify the corresponding angles

Since \(S\) corresponds to \(Z\) in similar triangles \(PRS\) and \(XYZ\), \(\angle Z=\angle S\)

Step3: Find the measure of \(\angle S\)

From the triangle \(PRS\), \(\angle S = 23^{\circ}\) (given in the figure)

Answer:

D. \(23^{\circ}\)