Question

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.

Answer 1

Let the measure of angle A is x

then the measure of B

`B=(3)/(5)(180-x)`

The measure of C is

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

Now

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

So

`\begin{gathered} \angle A=80 \\ \angle B=(3)/(5)*100=60 \\ \angle C=(4)/(3)*30=40 \end{gathered}`