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

Finding the measure of the smallest angle:

The ratio of the angles is $3:5:9:13,$.

Then, assume the angles to be $3x,5x,9x\text{and}13x$.

Applying the angle-sum property of a quadrilateral,

$$\begin{gathered} 3x+5x+9x+13x={360}^{\circ } \\ \Rightarrow 30x={360}^{\circ } \\ \Rightarrow x=\frac{360}{30} \\ \Rightarrow x={12}^{\circ } \end{gathered}$$

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

Hence, the measure of the smallest angle is ${36}^{\circ }$.