Question

find the measures of two complementary angles if the difference between the measures of the two angles is 49°.

Explanation:

Step1: Define the angles

Let one angle be $x$ and the other be $y$. Since they are complementary, $x + y=90^{\circ}$. Also, given that $|x - y| = 49^{\circ}$. Assume $x>y$, so $x - y=49^{\circ}$.

Step2: Solve the system of equations

We have the system of equations

$$\begin{cases}x + y=90\\x - y=49\end{cases}$$

. Add the two equations together: $(x + y)+(x - y)=90 + 49$. Simplifying gives $2x=139$, so $x=\frac{139}{2}=69.5^{\circ}$.

Step3: Find the second - angle

Substitute $x = 69.5^{\circ}$ into $x + y=90^{\circ}$. Then $69.5+y=90$, and $y=90 - 69.5 = 20.5^{\circ}$.

Answer:

$69.5$ and $20.5$