Question

Find the measure of each angle.

The ratio of the measures of two supplementary angles is$11:4$.

Short answer

The measure of each angle is ${132}^{\circ }$and${48}^{\circ }$ .

Step-by-step solution

Step 1. Given information.

The ratio between angles of two supplementary angles is,

$11:4$

Step 2. Concept used.

The sum of angles supplementary angles is${180}^{\circ }$

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

It might not represent the actual measure.

Step 3. Consider the angles as11x and4x .

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

$\begin{array}{c}11x+4x=180\\ 15x=180\\ x=12\end{array}$

So each of the angles are given by,

$\begin{array}{c}11x=11\times 12\\ 11x=132\end{array}$

And,

$\begin{array}{c}4x=4\times 12\\ 4x=48\end{array}$

Therefore, the measure of each angle is ${132}^{\circ }$and${48}^{\circ }$.