Question

24 quadrilateral pqrs is similar to quadrilateral pqrs, where p, q, r, and s correspond to p, q, r, and s, respectively. the measure of angle p is 30°, the measure of angle q is 50°, and the measure of angle r is 70°. the length of each side of pqrs is 3 times the length of each corresponding side of pqrs. what is the measure of angle p? a) 10° b) 30° c) 40° d) 90°

Explanation:

Step1: Recall property of similar polygons

Similar polygons have equal - corresponding angles.

Step2: Identify corresponding angles

Since quadrilateral \(P'Q'R'S'\) is similar to quadrilateral \(PQRS\) and \(P\) corresponds to \(P'\), \(\angle P=\angle P'\).

Step3: Substitute the given angle measure

Given that \(\angle P = 30^{\circ}\), so \(\angle P'=30^{\circ}\).

Answer:

B. \(30^{\circ}\)