Question

Two supplementary angles have measures in the ratio 5:4 what is the measure of the smaller angle

Answer 1

The smaller one measures 80 degrees.

Step-by-step explanation:

We are given:

`a+b=180`

`(a)/(b)=(5)/(4)`

So we have a system to solve.

I'm going to solve the bottom equation for
`a` by multiplying
`b` on both sides:

`a=(5)/(4)b`.

Let's plug this into the first equation:
`a+b=180`:

`(5)/(4)b+b=180`

`(5)/(4)b+(4)/(4)b=180`

`(9)/(4)b=180`

Multiply both sides by 4/9:

`b=(4)/(9) \cdot 180`

`b=\4 \cdot (180)/(9)`

`b=4 \cdot 20`

[texb=80[/tex].

This means
`a=(5)/(4) \cdot 80=5 \cdot (80)/(4)=5 \cdot 20=100`.

We do have
`100+80=180 \text{ and } (100)/(80)=(5)/(4)`.

So the smallest of the two angles is the one that measures 80 degrees.

The one that is the larger of the two is the one that measures 100 degrees.