Question

Complete the activity. ▭ABCD is a parallelogram. If ∠A = (4x + 13)° and ∠D = (5x – 22)° then find the measure of ∠B. Solution: ▭ABCD is a parallelogram. Adjacent angles of a parallelogram are ∠A and ∠D are adjacent angles. ⸫ (4x + 13)° + (5x – 22)° = ⸫ 9x – 9 = 180° ⸫ 9x = 189° ⸫ x = ⸫ ∠B = ∠D (opposite angles) ⸫ ∠B =​

Answer 1

Answer:

Angle A and angle D are the adjacent angles.

And we know that,

Adjacent angles of a parallelogram are supplementary.

hence,

==> (4x + 13)° + (5x - 22)° = 180

==> 9x - 9 = 180

==>9x= 180 + 9

==> 9x = 189

-

==> x = 21

Therefore, the angles will be.

angle A = 4x + 13

==> 4* 21 + 13

==> 84 +13

==> 97°

angle D = 5x - 22

==> 5*21- 22

==> 105 - 22

==> 83°

And we know that the opposite side and opposite angles of a parallelogram are congruent.

Therefore,

Angle C = 97°

Angle B = 83°

Thanks..