Question

Two adjacent angles of a parallelogram are (3x - 4) and (3x + 16).
Find the value of x and hence find the measure of each of its angles.​

Answer 1

Answer:

3x - 4) = 80 degrees

(3x + 16) = 100 degrees.

Step-by-step explanation:

The two adjacent angles of a parallelogram = 180 degrees.

Therefore (3x - 4) + ( 3x + 16) = 180

6x + 12 = 180

6x = 180 - 12

6x = 168

 

x = 168/6

x = 28 degrees

Therefore (3x - 4) = 80 degrees

(3x + 16) = 100 degrees.

Answer 2

Answer:

Step-by-step explanation:

In parallelogram the adjacent interior angles are complementary.

i.e.

(3x-4) + (3x+16) = 90°

Opening up the brackets on the LHS:

3x-4+3x+16 = 90°

6x + 12 = 90°

Send 12 to RHS:

6x = 90° - 12

6x = 78°

Send 6 to RHS

x = 78/6 = 13°

Therefore, x = 13°

THE ANGLES OF THE PARALLELOGRAM ARE:

3x - 4 = 3*13° - 4

= 39° - 4

= 35°

And

3x + 16 = 3 * 13 + 16

= 39 + 16

= 55°

Therefore, x = 13° and the two adjacent angles of the parallelogram are 35° and 55°.