Question

Two angles are supplementary. The measure of one angle is 10° more than three times the other. Find the measure of each angle

Answer 1

The measure of angles are 137.5 degrees and 42.5 degrees

Solution:

Given that two angles are supplementary

Let "a" be the one of supplementary angle

Let "b" be the other supplementary angle

Given that measure of one angle is 10 degree more than three times the other

measure of one angle = 10 + three times the other angle

a = 10 + 3b ---- eqn 1

We know that,

Two Angles are Supplementary when they add up to 180 degrees.

a + b = 180 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "b"

Substitute eqn 1 in eqn 2

10 + 3b + b = 180

10 + 4b = 180

4b = 170

b = 42.5

From eqn 1,

a = 10 + 3(42.5)

a = 10 + 127.5 = 137.5

a = 137.5

Thus the measure of angles are 137.5 degrees and 42.5 degrees