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

1. User Answers freckledspots
Answer:
The smaller one measures 80 degrees.
Stepbystep explanation:
We are given:
[tex]a+b=180[/tex]
[tex]\frac{a}{b}=\frac{5}{4}[/tex]
So we have a system to solve.
I'm going to solve the bottom equation for [tex]a[/tex] by multiplying [tex]b[/tex] on both sides:
[tex]a=\frac{5}{4}b[/tex].
Let's plug this into the first equation: [tex]a+b=180[/tex]:
[tex]\frac{5}{4}b+b=180[/tex]
[tex]\frac{5}{4}b+\frac{4}{4}b=180[/tex]
[tex]\frac{9}{4}b=180[/tex]
Multiply both sides by 4/9:
[tex]b=\frac{4}{9} \cdot 180[/tex]
[tex]b=\4 \cdot \frac{180}{9}[/tex]
[tex]b=4 \cdot 20[/tex]
[texb=80[/tex].
This means [tex]a=\frac{5}{4} \cdot 80=5 \cdot \frac{80}{4}=5 \cdot 20=100[/tex].
We do have [tex]100+80=180 \text{ and } \frac{100}{80}=\frac{5}{4}[/tex].
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.