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?
$\boldsymbol{100}$°

1. move point c so the measure of arc ac is 50°. what is the measure of $angle abc$?

$\boldsymbol{square}$°

Explanation:

Step1: Recall inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. The formula is $m\angle ABC = \frac{1}{2}m\overset{\frown}{AC}$

Step2: Substitute given arc measure

We know $m\overset{\frown}{AC}=50^\circ$. Plug into the formula:
$m\angle ABC = \frac{1}{2} \times 50^\circ$

Step3: Calculate the angle measure

$m\angle ABC = 25^\circ$

Answer:

$25$