Question

the measure of an angle is 148.6°. what is the measure of its supplementary angle?

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles add up to 180°. Let the given angle be $\theta = 148.6^{\circ}$, and its supplementary - angle be $\alpha$. Then $\theta+\alpha = 180^{\circ}$.

Step2: Solve for the supplementary angle

We can find $\alpha$ by subtracting $\theta$ from 180°. So, $\alpha=180^{\circ}-\theta$. Substitute $\theta = 148.6^{\circ}$ into the formula: $\alpha = 180 - 148.6$.
$\alpha=31.4^{\circ}$

Answer:

$31.4^{\circ}$