Question

an angle measures 49.8° more than the measure of its complementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Define variables

Let the measure of the complementary angle be $x$ degrees. Then the other angle is $x + 49.8$ degrees.

Step2: Use complementary angle property

Since complementary angles add up to $90^\circ$, we have the equation $x+(x + 49.8)=90$.

Step3: Solve the equation

Simplify the left side: $2x+49.8 = 90$.
Subtract $49.8$ from both sides: $2x=90 - 49.8=40.2$.
Divide both sides by 2: $x=\frac{40.2}{2}=20.1$.

Step4: Find the other angle

The other angle is $x + 49.8=20.1+49.8 = 69.9$.

Answer:

$20.1^\circ$ and $69.9^\circ$