Question

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

Answer 1

Answer:

The smaller one measures 80 degrees.

Step-by-step explanation:

We are given:

$a+b=180$

$\frac{a}{b}=\frac{5}{4}$

So we have a system to solve.

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

$a=\frac{5}{4}b$.

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

$\frac{5}{4}b+b=180$

$\frac{5}{4}b+\frac{4}{4}b=180$

$\frac{9}{4}b=180$

Multiply both sides by 4/9:

$b=\frac{4}{9} \cdot 180$

$b=\4 \cdot \frac{180}{9}$

$b=4 \cdot 20$

[texb=80[/tex].

This means $a=\frac{5}{4} \cdot 80=5 \cdot \frac{80}{4}=5 \cdot 20=100$.

We do have $100+80=180 \text{ and } \frac{100}{80}=\frac{5}{4}$.

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.