Question

Quadrilateral abcd and quadrilateral pqrs are similar. The lengths of ab and cd are 15 units each, and the lengths of ad and bc are 10 units each. Use the given information to complete the following sentences. If the length of pq is 6 units, then the length of ps is 5 units. If m∠adc is 62° and m∠bcdis 118°, then m∠qrs is

A) 58°
B) 72°
C) 118°
D) 180°

Answer 1

By setting up proportions and using the given information about the lengths of the sides of quadrilateral ABCD and quadrilateral PQRS, we can find the measure of angle QRS to be 58°.

Step-by-step explanation:

Given that quadrilateral ABCD and quadrilateral PQRS are similar, we can use the given information to find the measure of angle QRS, denoted as m∠QRS.

Since the lengths of AB and CD are 15 units each, and the lengths of AD and BC are 10 units each, we can say that the corresponding sides of the two quadrilaterals are in proportion.

This means that AB/PQ = BC/QR = CD/RS. Using the given length of PQ as 6 units, we can find the length of QR by setting up the proportion: 15/6 = 10/QR.

Solving for QR, we get QR = 4 units. Since angles in similar figures are congruent, m∠QRS is equal to the measure of angle ADC, which is given as 62°. Therefore, the answer is A) 58°.