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? 100
2. move point c so the measure of arc ac is 50°. what is the measure of ∠abc?

m∠abc = 52°
m⌢ac = 104°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its 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 inscribed - angle

Given $m\overset{\frown}{AC} = 50^{\circ}$, using the formula $m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}$, we substitute the value of the arc measure. So $m\angle ABC=\frac{1}{2}\times50^{\circ}$.

Answer:

$25$