Question

Three angles of a quadrilateral are in the ratio $3:5:8.$ The mean of these angles is ${80}^{\circ }.$ Find all the four angles of the quadrilateral.

Answer 1

Let angles be $a,b,c$ & $d$ resp.

$\frac{a}{b}=\frac{3}{5},\frac{b}{c}=\frac{5}{8}$

Now, $\frac{a+b+c}{3}=80\Rightarrow \frac{\left(3b/5\right)+b+\left(8b/5\right)}{3}=80$

$\Rightarrow \left(166/5\right)=240\Rightarrow b={75}^0$

So, $a={45}^0,c={120}^0\&d=360-(a+b+c)$

$\Rightarrow d={120}^0$