Question

In the following exercises, translate to a system of equations and solve.

Two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle. Find the measures of both angles.

Short answer

The larger and smaller angles are 74 and 16 degrees respectively.

Step-by-step solution

Step 1. Given Information 

The given data is that two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle.

Step 2. Calculation  

Let x be the larger angle and y be the smaller angle.

The measure of the larger angle is ten more than four times the measure of the smaller angle that is$x=4y+10°--\left(1\right)$

Also, the angles are complementary that is$x+y=90°--\left(2\right)$

Substitute the value of x from equation (1) to equation (2) and solve.

$$\begin{gathered} 4y+10°+y°=90° \\ 5y=80° \\ y=16° \end{gathered}$$

Substitute the value of y in equation (1) to find the value of x.

$$\begin{gathered} x=4(16°)+10° \\ x=64°+10° \\ x=74° \end{gathered}$$