Question

One supplementary angle is 15 degrees less than twice the other. Find the measure of the two supplementary angles.

Answer 1

The measure of the two supplementary angles are 65 degrees and 115 degrees.

Explanation:

The sum of supplementary angles is equal to 180 degrees. Let x and y are two angles such that,

`x+y=180\ ....(1)`

According to given condition,

One supplementary angle is 15 degrees less than twice the other, it means,

`x=2y-15\ .....(2)`

Putting the value of x from above equation in equation (1),

`2y-15+y=180\\\\3y-15=180\\\\3y=195\\\\y=(195)/(3)\\\\y=65^(\circ)`

Now put the value of y in equation (1), so,

`x+65=180\\\\x=115^(\circ)`

So, the measure of the two supplementary angles are 65 degrees and 115 degrees.