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 inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc. That is, if $\angle ABC$ is an inscribed angle and $\overset{\frown}{AC}$ is the intercepted arc, then $m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}$.

Step2: Solve for the measure of the arc

We are given that $m\angle ABC = 50^{\circ}$. Using the formula $m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}$, we can solve for $m\overset{\frown}{AC}$ by multiplying both sides of the equation by 2. So, $m\overset{\frown}{AC}=2\times m\angle ABC$.
Substituting $m\angle ABC = 50^{\circ}$ into the equation, we get $m\overset{\frown}{AC}=2\times50^{\circ}=100^{\circ}$.

Answer:

$100$