Question

Find the measure of each angle.

The ratio of the measures of two complementary angles is$4:5$.

Short answer

The measure of each angle is ${40}^{\circ }$and${50}^{\circ }$.

Step-by-step solution

Step 1. Given information.

The ratio between angles of two complementary angles is,

$4:5$

Step 2. Concept used.

The sum of complementary angles is${90}^{\circ }$.

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

It might not represent the actual measure.

Step 3. Consider the angles as4x and 5x.

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

$\begin{array}{c}4x+5x=90\\ 9x=90\\ x=10\end{array}$

So each of the angles are given by,

$\begin{array}{c}4x=4\times 10\\ \text{4x}=40\end{array}$

And,

$\begin{array}{c}5x=5\times 10\\ \text{5x}=50\end{array}$

Therefore, the measure of each angle is${40}^{\circ }$ and${50}^{\circ }$.