Question

An angle measures 40.2° more than the measure of its complementary angle. What is the measure of each angle?

Answer 1

Solving for the measurements of Complementary Angles

Answer:

$24.9^{\circ}$ and $65.1^{\circ}$

Step-by-step explanation:

Recall that Angles that are complementary to each other add up to $90^{\circ}$.

Let $a$ be the measure of the complementary angle.

If an angle is $40.2^{\circ}$ more than its complementary angle, the measure of that angle is $a +40.2$. The sum of both angles are expressed $a +(a +40.2)$ but since the have to add to $90$ as they are complementary, $a +(a +40.2) = 90$.

Solving for $a$:

$a +(a +40.2) = 90 \\ a +a +40.2 = 90 \\ 2a +40.2 = 90 \\ 2a +40.2 -40.2 = 90 -40.2 \\ 2a = 49.8 \\ \frac{2a}{2} = \frac{49.8}{2} \\ a = 24.9$

Since the other angle measures $a +40.2$, we can plug in the value of $a$ to find the measure of the angle.

Evaluating $a +40.2$:

$a +40.2 \\ 24.9 +40.2 \\ 65.1$

The measure of the angles are $24.9^{\circ}$ and $65.1^{\circ}$