Question

Given that ABCD is a parallelogram, find each of the following

AB
AD
< A
< D

Answer 1

AB = 8

AD = 10

m∠A = 28°

m∠D = 62°

Explanation:

A few facts to remember about a parallelogram.

1. Opposites sides are congruent

2. Opposites angles are congruent

3. Consecutive angles are complementary

So, AB = 8, AD = 10, m∠A = 90 - 62 = 28°, m∠D = 62°

Answer 2

AB = 8

AD = 10

<A = 118

<D = 62

Explanation:

1. AB

Because opposite sides in a parallelogram are equal, DC = AB = 8.

2. AD

Because opposite sides in a parallelogram are equal, BC = AD = 10.

3. <A

Adjacent angles are supplementary in a parallelogram, so A = 180 - 62 = 118

4. <D

Opposite angles are equal in a parallelogram, so B = D = 62