Question

Two angles are supplementary. One angle is 5 degrees less than four times the other. What are the measures of the angles?

Answer 1

`a=143^o`, `b=37^o`

Explanation:

To be able to answer this, we must know what it means that the angles are supplementary. If you have two angles a and b and
`a+b=180^o`, they are supplementary.

As `a=4b-5^o`,
`a+b=4b-5^o + b=5b-5^o=180^o`
which gives `b=185^o/5=37^o`
Therefore `a=180^o - b= 143^o`

Answer 2

`color(blue)(143^@, 37^@)`

Explanation:

Let the angle be `theta`

One angle is 5 degrees less than four times the other.

One angle is `4theta-5`

The other angle is `theta`

Supplementary implies:

`4theta-5+theta=180=>theta=37`

So the angles are:

`4(37)-5=143^@`

`37^@`