Question

∠J

and ∠K


are consecutive angles in a parallelogram, m∠J=(3x+7)°


, and m∠K=(5x−11)°


.

Answer 1

x = 23°

Explanation:

In a parallelogram, sum of consecutive angles (adjacent angles) are supplementary.

m∠J + m∠K = 180

3x + 7 + 5x - 11 = 180

3x + 5x + 7 - 11 = 180

Combine like terms,

8x - 4 = 180

Add 4 to both sides,

8x = 180 + 4

8x = 184

Divide both sides by 8,

x = 184÷ 8

x = 23°

m∠J = 3x + 7

= 3*23 + 7

= 69 + 7

= 76°

m∠K = 5x -11

= 5*23 - 11

=115 - 11

= 104°