Question

The angles of quadrilateral are in the ratio $3:5:9:13$. Find all the angles of the quadrilateral.

Answer 1

Let $ABCD$ be a quadrilateral in which $\angle A$ : $\angle B$ : $\angle C$ : $\angle D$ = $3:5:9:13$

Sum of the ratios $=3+5+9+13=30$

Also , $\angle A$ + $\angle B$ + $\angle C$ + $\angle D$ = ${360}^o$

Sum of all the angles of quadrilateral is ${360}^o$.

$\therefore \angle A=\frac{3}{30}\times {360}^o={36}^o$

$\angle B=\frac{5}{30}\times {360}^o={60}^o$

$\angle C=\frac{9}{30}\times {360}^o={108}^o$

$\angle D=\frac{13}{30}\times {360}^o={156}^o$