Question

If the angles of quadrilateral are in the ratio $3:5:9:13$, find the value of smallest angle of quadrilateral.

Answer 1

By the angle sum property, sum of the angles in a quadrilateral $={360}^{\circ }$

Given : Angles in a quadrilateral are $3x,5x,9x$ and $13x$

Sum of all angles $3x+5x+9x+13x={360}^{\circ }$

$\Rightarrow 30x={360}^{\circ }$

$\Rightarrow x=\frac{{360}^{\circ }}{30}={12}^{\circ }$

The smallest angle is $3x=3\times {12}^{\circ }={36}^{\circ }$