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

1 Answer

  • Answer:

    The smaller one measures 80 degrees.

    Step-by-step explanation:

    We are given:



    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:


    Let's plug this into the first equation: [tex]a+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]


    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.