Question

explore the properties of inscribed angles by following these steps. what is the measure of ∠abc? 3. make a conjecture. which measures will change if you move vertex b of the inscribed angle? 4. move vertex b and observe what happens to the angle measures. was your conjecture correct? m∠abc = 52° m(widehat{ac}) = 104°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Given $m\widehat{AC}=104^{\circ}$, and $\angle ABC$ is an inscribed angle intercepting $\widehat{AC}$.

Step2: Calculate the measure of $\angle ABC$

$m\angle ABC=\frac{1}{2}m\widehat{AC}$. Substitute $m\widehat{AC} = 104^{\circ}$ into the formula: $m\angle ABC=\frac{1}{2}\times104^{\circ}=52^{\circ}$.

Answer:

$52^{\circ}$