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°

m∠J = 159.4°
m∠K = 3.8°
m∠L = 16.8°

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