Question

The angles of a quadrilateral are in the ratio $2:3:5:8$. Find the smallest angle of the quadrilateral.

Answer 1

Given ratio of angles of quadrilateral $ABCD$ is $2:3:5:8$

Let the angles of quadrilateral $ABCD$ be $2x,3x,5x,8x$, respectively.

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

$\Rightarrow 2x+3x+5x+8x={360}^o$

$\Rightarrow 18x={360}^o$

$\therefore x={20}^o$.

$\therefore \angle A=2x=2\times {20}^o={40}^o$,

$\angle B=3x=3\times {20}^o={60}^o$,

$\angle C=5x=5\times {20}^o={100}^o$

and $\angle D=8x=8\times {20}^o={160}^o$.

$\therefore$ The smallest angle $={40}^o$.