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In triangle ABC, the measure of angle B is three fifths the measure of the supplement of angle A. The measure of angle C is four thirds the measure of the complement of angle B. Find the degree measure of the three angles of the triangle.

Respuesta :

Let the measure of angle A is x

then the measure of B

[tex]B=\frac{3}{5}(180-x)[/tex]

The measure of C is

[tex]\begin{gathered} C=\frac{4}{3}(90-\frac{3}{5}(180-x)) \\ =120-\frac{4}{5}(180-x) \\ =120-144+\frac{4}{5}x \end{gathered}[/tex]

Now

[tex]\begin{gathered} x+(108-\frac{3}{5}x)+(\frac{4}{5}x-24)=180 \\ x-\frac{3}{5}x+\frac{4}{5}x+84=180 \\ \frac{6}{5}x=96 \\ x=80 \end{gathered}[/tex]

So

[tex]\begin{gathered} \angle A=80 \\ \angle B=\frac{3}{5}\times100=60 \\ \angle C=\frac{4}{3}\times30=40 \end{gathered}[/tex]

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