Question

18 mark for review
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^{circ} ), the measure of angle ( q ) is ( 50^{circ} ), and the measure of angle ( r ) is ( 70^{circ} ). 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^{circ} )
b ( 30^{circ} )
c ( 40^{circ} )
d ( 90^{circ} )

Explanation:

Step1: Recall the property of similar polygons

Similar polygons have corresponding angles equal.

Step2: Identify the corresponding angles

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

Answer:

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