Question

Quadrilateral ABCD is parallelogram. Angle A=(4x+13)° and angle B = (5x-22)°.Find measure of A​

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°

Thank You =)