Question

the measure of an angle is 74°. what is the measure of its supplementary angle?

Explanation:

Step1: Recall supplement - angle definition

The sum of an angle and its supplementary angle is 180°. Let the given angle be $\theta = 74^{\circ}$ and its supplementary angle be $\alpha$. Then $\theta+\alpha = 180^{\circ}$.

Step2: Solve for the supplementary angle

We can find $\alpha$ by subtracting the given angle from 180°. So, $\alpha=180^{\circ}-\theta$. Substitute $\theta = 74^{\circ}$ into the formula: $\alpha = 180^{\circ}-74^{\circ}=106^{\circ}$.

Answer:

$106^{\circ}$