Q. 103 - Intermediate Algebra

Question

Two angles are supplementary. The measure of the larger angle is five less than four times the measure of the smaller angle. Find the measure of both angles. 

Step-by-Step Solution

Answer

The measures of angle are $143$ and $37$.

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,

$x+y=180$

Step 2. Creating the equation

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

Therefore, $x=4y-5$

Step 3. Finding the value y

Substitute the value of $x=4y-5$ in the equation $x+y=180$

Therefore,

          $x+y=180$

$4y-5+y=180$

      $5y-5=180$

              $5y=180+5$

$5y=185$

$y=\frac{185}{5}$

  $=37$

Step 4. Finding the value

Put, $y=37$ into $x=4y-5$ and solve for x

$x=4y-5$

   $$\begin{gathered} =148-5 \\ =143 \end{gathered}$$