Question

The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle.​

Answer 1

The measure of the angle is 15 degree.

Explanation:

The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle.

Supplementary angles are those that add up to 180, and complementary angles add up to 90.

Let
`x` represent the angle.

`(180^(\circ) - x)` is the supplementary angle and
`(90^(\circ)-x)` is the complementary angle.

`180^(\circ)-x=3(90^(\circ)-x)-60^(\circ)\\180^(\circ)-x=270^(\circ)-3x-60^(\circ)\\180^(\circ)-x+3x=210^(\circ)\\2x=30^(\circ)\\x=15^(\circ)`

`(90-15)^(\circ)=75^(\circ)` is the complementary

`(180-15)^(\circ)=165^(\circ)` is the supplementary angle