Question

explore the properties of inscribed angles by following these steps. 1. move point c so the measure of the inscribed angle abc is 50°. what is the measure of arc ac? m∠abc = 52° mac = 104°

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Let the measure of the inscribed angle $\angle ABC=\theta$ and the measure of the arc $AC = s$. Then $\theta=\frac{1}{2}s$.

Step2: Solve for the measure of the arc

Given $\theta = 50^{\circ}$, we can solve for $s$ by rearranging the formula $s = 2\theta$. Substituting $\theta = 50^{\circ}$ into the formula, we get $s=2\times50^{\circ}=100^{\circ}$.

Answer:

$100^{\circ}$