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? (a box for answer)° (an image of a circle with points a, b, c on it, and text: 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. So, if \( m\angle ABC = 50^\circ \), then the measure of arc \( AC \) is twice the measure of \( \angle ABC \).

Step2: Calculate arc AC measure

Using the formula \( m\widehat{AC}=2\times m\angle ABC \), substitute \( m\angle ABC = 50^\circ \). So, \( m\widehat{AC}=2\times50^\circ = 100^\circ \).

Answer:

\( 100 \)