Question

If the angles of a quadrilateral are in the ratio 3 :5 : 9 : 13. Then find the measure of the smallest angle.

Answer 1

Ratio in the angles of a quadrilateral

= 3 :5: 9: 13

Let firat angle = 3x

Second angle = 5x

Third angle = 9x

and fourth angle = 13x

$\because$ The sum of angles of a quadrilateral = ${360}^{\circ }$

$\therefore 3x+5x+9x+13x={360}^{\circ }$

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

$\therefore$ Smallest angle = $3x=3\times {12}^{\circ }={36}^{\circ }$