Mathematics

Question

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:

    [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.

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