Question

The angles of a quadrilateral $ABCD$ are in the ratio $4 : 9 : 10: 13$. Find the angles.

Answer 1

Let the measures of $\angle A,\angle B,\angle C$ and $\angle D$ be 4x, 9x, 10x and 13x respectively.
$\therefore \angle A+\angle B+\angle C+\angle D={360}^o$
$\Rightarrow 4x+9x+10x+13x={360}^o$
$\Rightarrow 36x={360}^o\Rightarrow x=\frac{{360}^o}{{36}^o}={10}^o$
Hence, $\angle A=4\times {10}^o={40}^o$
$\angle B=9\times {10}^o={90}^o$
$\angle C=10\times {10}^o={100}^o$
$\angle D=13\times {10}^o={130}^o$
Thus, the four angles of the quadrilateral are ${40}^o,{90}^o,{100}^o$ and ${130}^o$