Answer:
x = 8
m∠M = 52°
m∠K = 52°
m∠L = 128°
m∠J = 128°
Explanation:
If the given shape is a parallelogram, its opposite interior angles are equal.
⇒ m∠M = m∠K
⇒ 7x - 4 = 5x + 12
Subtract 5x from both sides:
⇒ 2x - 4 = 12
Add 4 to both sides:
⇒ 2x = 16
Divide both sides by 2:
⇒ x = 8
Substitute found value of x into the expressions for each angle to find the measures of the angles:
⇒ m∠M = 7(8) - 4 = 52°
⇒ m∠K = 5(8) + 12 = 52°
As the angles on the same side of the transversal in a parallelogram sum to 180°, then
⇒ m∠J + m∠M = 180°
⇒ m∠J = 180° - m∠M
⇒ m∠J = 180° - 52°
⇒ m∠J = 128°
As m∠L = m∠J then m∠L = 128°