Question

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

Answer 1

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!

Answer 2

Solution :-

Sum of the measures of the adjacent angles of a parallelogram is 180°

Given - ∠ A = (3x + 12)° and ∠ B = (2x - 32)°

⇒ 3x + 12 + 2x - 32 = 180

⇒ 5x = 180 + 32 - 12

⇒ 5x = 200

⇒ x = 200/5

⇒ x = 40

So, the value of x is 40

Now, substituting the value of x = 40 in (3x + 12)° and (2x - 32)°

⇒ (3*40) + 12

⇒ 120 + 12

= 132°

So, ∠ A is 132°

⇒ (2*40) - 32

⇒ 80 - 32

= 48°

So, ∠ B = 48°

As the opposite angles of a parallelogram are of equal measure. So, ∠ C = 132° and ∠ D = 48°

Answer.