Question

The difference of two

complementary angles is 17

degrees. Find the measures of the

angles.

Short answer

The measures of angle are$53.5$and$36.5$

Step-by-step solution

Step 1. Given information

Two complementary angle $x$and $y$such that $x+y=90$.

Step 2. Creating the equation

The difference of the two complementary angles is 17 degrees.

therefore,

$x-y=17$

Step 3. Solve for y

Put the values of $x=17+y$into

$$\begin{gathered} x+y=90 \\ 17+y+y=90 \\ 2y=90-17 \\ y=\frac{73}{2} \\ y=36.5 \end{gathered}$$

Step 4. Solve for x

Put the value of $y=36.5$into

$$\begin{gathered} x+y=90 \\ x+36.5=90 \\ x=53.5 \end{gathered}$$