Question

Use the Diagram of Parallelogram ABCD to find each value. (Show how you found each value please.)

1. angle A = 180-127=53

2. angle D

3.x

4. AB

Answer 1

The answers are

1) ∠A = 53 °

2) ∠D = 127°

3) x = 5

4) AB = 7

Explanation:

In parallelogram,

• Consecutive angles are supplementary (∠A + ∠B = 180°).
• Opposite angels are congruent (∠D = ∠B).
• Opposite sides are congruent (AB = DC).

1) find angle A :

Given, ∠B = 127°

∠A + ∠B = 180°

∠A = 180-127= 53 °

2) find angle D :

Given, ∠B = 127°

∠D = ∠B

∠D = 127°

3) find x :

AB = DC

(x+2) = (2x-3)

2+3 = 2x-x

x = 5

4) find AB :

AB = (x+2)

AB = 5+2

AB = 7