Question

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

• A. ${24}^{\circ }$
• B. ${36}^{\circ }$
• C. ${37}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${36}^{\circ }$

Let the angles be $3x,5x,9x,13x.$
Since the sum of four angles of a quadrilateral is ${360}^{\circ }.$
Therefore,
$3x+5x+9x+13x={360}^{\circ }$
$\Rightarrow 30x={360}^{\circ }$
$\Rightarrow x=\frac{{360}^{\circ }}{30}$
$\Rightarrow x={12}^{\circ }$
Thus the smallest angle is
$=3x=3\times 12={36}^{\circ }.$