Question

2) In a parallelogram ABCD, if angle A =(3x + 12)° and angle B=(2x-32)
then find the value of x and then find the
measures of angle C and angle D.​

Answer 1

Step-by-step explanation:

Given Two angles of a parallelogram are (3x + 12) and (2x - 32).

We know that the sum of adjacent angles of a parallelogram is 180.

=> (3x + 12) + (2x - 32) = 180

=> 3x + 12 + 2x - 32 = 180

=> 5x - 20 = 180

=> 5x = 180 + 20

=> 5x = 200

=> x = 40.

Now,

The measure of angle A = 3x + 12

= 3(40) + 12

= 120 + 12

= 132.

The measure of angle B = 2x - 32

= 2(40) - 32

= 80 - 32

= 48.

We know that the opposite angles of a parallelogram are equal.

Hence, the measure of angle C = 132.

Hence, the measure of angle D = 48.

Therefore, the angles are A = 132, B = 48, C = 132, D = 48.

Hope this helps!