Question

find the measure of ∠d, and the perimeter and area of parallelogram abcd.
∠d = 152°, p = 74 centimeters, a = 160 square centimeters
∠d = 62°, p = 37 centimeters, a = 340 square centimeters
∠d = 62°, p = 37 centimeters, a = 160 square centimeters
∠d = 162°, p = 74 centimeters, a = 340 square centimeters

Explanation:

Step1: Find measure of ∠D

In a parallelogram, consecutive angles are supplementary. Given ∠A = 28°, so ∠D = 180° - 28° = 152°.

Step2: Find perimeter (P)

In parallelogram ABCD, opposite sides are equal. AB = 17 cm, AD = 20 cm. Perimeter P = 2(AB + AD) = 2(17 + 20) = 2*37 = 74 cm.

Step3: Find area (A)

Area of parallelogram = base height. Base AD = 20 cm, height = 8 cm. So A = 208 = 160 cm².

Answer:

∠D = 152°, P = 74 centimeters, A = 160 square centimeters