Question

The supplement of the measurement of an angle is 16 degrees less than three times the angle. Find the measurement of the angle and the supplement.

Answer 1

The measure of angle is 49 degrees and measure of supplement of angle is 131 degrees

Solution:

Let the angle be "x"

Let the measure of supplement of angle is "y"

Supplementary angles are two angles whose sum is 180 degrees

Therefore,

x + y = 180 ----- eqn 1

The supplement of the measurement of an angle is 16 degrees less than three times the angle

y = 3x - 16 --------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

x + 3x - 16 = 180

4x = 180 + 16

4x = 196

Divide both sides of equation by 4

x = 49

Substitute x = 49 in eqn 2

y = 3(49) - 16

y = 147 - 16

y = 131

Thus the measure of angle is 49 degrees and measure of supplement of angle is 131 degrees