Question

An angle measures 149.2° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Solving for the measurements of Complementary Angles

Answer:

$15.4^{\circ}$ and $164.6^{\circ}$

Step-by-step explanation:

Recall that Angles that are supplementary to each other add up to $180^{\circ}$.

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

If an angle is $149.2^{\circ}$ more than its supplementary angle, the measure of that angle is $a +149.2$. The sum of both angles are expressed $a +(a +149.2)$ but since the have to add to $180$ as they are supplementary, $a +(a +149.2) = 180$.

Solving for $a$:

$a +(a +149.2) = 180 \\ a +a +149.2 = 180 \\ 2a +149.2 = 180 \\ 2a +149.2 -149.2 = 180 -149.2 \\ 2a = 30.8 \\ \frac{2a}{2} = \frac{30.8}{2} \\ a = 15.4$

Since the other angle measures $a +149.2$, we can plug in the value of $a$ to find the measure of the angle.

Evaluating $a +149.2$:

$a +149.2 \\ 15.4 +149.2 \\ 164.6$

The measure of the angles are $15.4^{\circ}$ and $164.6^{\circ}$