Question

exploring inscribed angles
explore the properties of inscribed angles by following these steps.

1. move point c so the measure of the inscribed angle abc is $50^\circ$.

what is the measure of arc ac?
$m\angle abc$
$m\overset{\frown}{ac} = 1$

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: Rearrange to solve for arc AC

Multiply both sides by 2 to isolate $m\overset{\frown}{AC}$: $m\overset{\frown}{AC} = 2 \times m\angle ABC$.

Step3: Substitute given angle value

Substitute $m\angle ABC = 50^\circ$: $m\overset{\frown}{AC} = 2 \times 50^\circ$.

Answer:

$100^\circ$