Question

The angles of a quadrilateral are in the ratio $1:2:3:4$. If the sum of the angles of a quadrilateral is ${360}^o$ , find the measure of the each angle.

Answer 1

Let the angles be a,b,c,d

$a:b:c:d=1:2:3:4$

Given $a+b+c+d=360$

$\frac{a}{1}=\frac{b}{2}=\frac{c}{3}=\frac{d}{4}=k$

$a=k,b=2k,c=3k,d=4k$

$a+b+c+d=10k=360$

$k=36$

$a=36;b=72;c=108;d=144$

If $\frac{a}{b}=\frac{5}{7}\to 1$

$\frac{b}{c}=\frac{14}{15}\to 2$

$1\times 2$

$\frac{a}{b}\times \frac{b}{c}=\frac{5}{7}\times \frac{14}{15}$

$\frac{a}{c}=\frac{2}{3}$