Question

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

Two angles are complementary. The measure of the larger angle is twelve less than twice the measure of the smaller angle. Find the measures of both angles.

Short answer

The larger and smaller angles are 56 and 34 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 twelve less than twice 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 twelve less than twice the measure of the smaller angle that is $x=2y-12°--\left(1\right)$

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.

$$\begin{gathered} 2y-12°+y=90° \\ 3y=102° \\ y=34° \end{gathered}$$

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

$$\begin{gathered} x=2(34°)-12° \\ x=68°-12° \\ x=56° \end{gathered}$$