Question

Find the measure of each angle.

The measure of the angles of a hexagon are in the ratio$4:5:5:8:9:9$ .

Short answer

The measure of each angle of the hexagon is, $72°,90°,90°,144°,162°,162°$.

Step-by-step solution

Step 1. Given Information.

The ratio between angles of a hexagon is,

$4:5:5:8:9:9$

Step 2. Concept used.

The sum of interior angles of a hexagon is, ${720}^{\circ }$.

A hexagon has six sides and six interior angles.

Since, ratio of the angles is always in the simplified form,

it might not represent the actual measure. So,

Step 3. consider the angles as and .

The sum of the angles of the hexagon can be expressed using the above relation as,

$\begin{array}{c}4x+5x+5x+8x+9x+9x=720\\ 40x=720\\ x=\frac{720}{40}\\ =18\end{array}$

So, each of the angles are given by,

$\begin{array}{c}4x=4\times 18\\ =72°\end{array}$

$\begin{array}{c}5x=5\times 18\\ =90°\end{array}$

$\begin{array}{c}8x=8\times 18\\ =144°\end{array}$

$\begin{array}{c}9x=9\times 18\\ =162°\end{array}$

Therefore, the angles of the hexagon are.$72°,90°,90°,144°,162°,162°$