Question

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

Answer 1

Given

The angles of a quadrilateral are in the ratio $3:5:9:13$

Let the common ratio between the angles be $x$

Let the angles be $3x,5x,9x$ and $13x$

By the Angle sum property of a quadrilateral

As we know that, the sum of the angles of a quadrilateral is $360°$

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

So the angles will be as follows:

$$\begin{gathered} 3x=3\times 12=36° \\ 5x=5\times 12=60° \\ 9x=9\times 12=108° \\ 13x=13\times 12=156° \end{gathered}$$

Hence, the angles of a quadrilateral are $36°,60°,108°and156°$