Question

Given parallelogram ABCD, find x and m< B

Answer 1

x = 38, ∠ B = 78°

Explanation:

Consecutive angles in a parallelogram are supplementary, then

3x - 12 + 2x + 2 = 180

5x - 10 = 180 ( add 10 to both sides )

5x = 190 ( divide both sides by 5 )

x = 38

Then

∠ D = 2x + 2 = 2(38) + 2 = 76 + 2 = 78°

The opposite angles in a parallelogram are congruent , so

∠ B = ∠ D = 78°

Answer 2

x = 38°

∠B = ∠D = 78°

Explanation:

3x - 12° + 2x + 2° = 180°

3x + 2x = 180° + 12° - 2°

5x = 190°|:5

x = 38°

∠B = ∠D = 2x + 2° = 78°