In triangle JKL, If angle L is thirteen more than angle K and angle J is seven times more than six times angle K, find the measure of each angle.

Refer to the diagram shown below.

Let

x = m∠J

y = m∠K

z = m∠L

Angle L is thirteen more than angle K, therefore

z = y + 13 (1)

Angle J is seven times more than six times angle K, therefore

x = 7 (6y) = 42y (2)

The sum of the angles in the triangle is 180°, therefore

x + y + z = 180 (3)

Substitute (1) and (2) into (3).

42y + y + (y + 13) = 180

44y + 13 = 180

44y = 167

y = 3.8°

x = 42y = 159.4°

z = y + 13 = 16.8°

Answer:

m∠J = 159.4°

m∠K = 3.8°

m∠L = 16.8°