Question

Two angles are complementary. The measure of

the larger angle is five more than four times the measure of the smaller angle. Find the measures

of both angles.

Short answer

The measures of the angles are$73$and$17$.

Step-by-step solution

Step 1. Given information

Two angles are complementary.

The measure of the larger angle is five more than four times the measure of the smaller angle.

Step 2. Forming linear equations

Let larger angle =$x$

Let smaller angle =$y$

Both the angles are complementary, So we get

$x+y=90$

Using the condition given, we get

$x=4y+5$

Step 3. Find value of angles

On substituting value of $x$from one equation to another, we get

localid="1644525555584" $$\begin{gathered} x+y=90 \\ 4y+5+y=90 \\ 5y+5=90 \\ 5y=85 \\ y=17 \end{gathered}$$

Now put value of $y$in any of the equation,

$$\begin{gathered} x+y=90 \\ x+17=90 \\ x=73 \end{gathered}$$

The measures of the angles are $73$ and$17$

Step 4. Check by substituting values in both the equations 

Substitute $x=73,y=17$in both the equations

$$\begin{gathered} x+y=90 \\ 73+17=90 \\ 90=90 \end{gathered}$$

This is true

$$\begin{gathered} x=4y+5 \\ 73=4\left(17\right)+5 \\ 73=68+5 \\ 73=73 \end{gathered}$$

This is also true