Question

the difference in the measures of two complementary angles is 39. (answer is a decimal)
what is the measure of the smaller angle?

Explanation:

Step1: Set up equations

Let the two complementary angles be $x$ and $y$ ($x>y$). Complementary angles sum to 90, so $x + y=90$. Also given $x - y=39$.

Step2: Solve the system of equations

Add the two equations: $(x + y)+(x - y)=90 + 39$. Simplifying gives $2x=129$, so $x=\frac{129}{2}=64.5$.

Step3: Find the smaller angle

Substitute $x = 64.5$ into $x + y=90$, we get $64.5+y=90$. Then $y=90 - 64.5=25.5$.

Answer:

$25.5$