Question

What is the measurement of an angle whose supplement is three times its complement?

Answer 1

`x=45degrees`

Explanation:

Let the angle to be solved be `x`
Let the supplement/compliment by `y`
`x+y=90` Complimentary angles add up to 90 degrees.
`x+3y=180` Supplementary angles add up to 180 degrees, the other angle is thrice the other compliment.

Evaluating this as a system:
`x+y=90` Isolate `x`:
`x=90-y` Input into the other equation:
`(90-y)+3y=180` Combine like terms, isolate `y` and its coefficients:
`2y=90` Isolate `y`
`y=45` Input into the first equation:
`x+45=90` Isolate `x`:
`x=45`degrees

Answer 2

The angle is 45°

Explanation:

Let the required angle be `x`.

Supplement of `x = (180°-x)`

Complement of `x = (90°-x)`

`=> 3 ×`complement of `x =3(90°-x)`

According to question;

Supplement of`x = 3 ×`complement of `x`

`=>(180°-x)=3(90°-x)`

`=>180°-x=270°-3x`

`=>-x+3x=270°-180°`

`=>2x=90°`

`=>x=45°`