Question

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 the angles.

Short answer

The measures of angles are $56$and$34$

Step-by-step solution

Step 1. Given information

Suppose $x$represents the measure of the first angle.

and similarly, $y$represents the measure of the second angle

Now, both the angles are complementary

Therefore,

$x+y=90$

Step 2. Creating the equation

The measures of the larger angle is twelve less than twice the measure of the smaller angle.

Therefore,$x=2y-12$

Step 3. Finding the value y

Substitute the value of $x=2y-12$in the equation $x+y=90$

Therefore,

$x+y=90$

$2y-12+y=90$

$3y-12=90$

$3y=90+12$

$3y=102$

$y=\frac{102}{3}$

$=34$

Step 4. Finding the value x

Put, $y=34$into $x=2y-12$and solve for x

$$\begin{gathered} x=2y-12 \\ x=2\left(34\right)-12 \end{gathered}$$

$$\begin{gathered} =68-12 \\ =56 \end{gathered}$$