Question

drag each tile to the correct box.
triangle abc is inscribed in a circle centered at point o.
order the measures of the three intercepted arcs from least to greatest.
$m\\ \widehat{bc}$ $m\\ \widehat{ab}$ $m\\ \widehat{ac}$

Explanation:

Step1: Recall Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc. For $\angle C = 63^\circ$, it intercepts arc $AB$. So, $m\widehat{AB}=2\times63^\circ = 126^\circ$.

Step2: Find the measure of arc $AC$

The total circumference of a circle is $360^\circ$. We know $m\widehat{BC}=118^\circ$ and $m\widehat{AB}=126^\circ$. Let $m\widehat{AC}=x$. Then $x + 118^\circ+ 126^\circ=360^\circ$. Solving for $x$: $x=360^\circ-(118^\circ + 126^\circ)=360^\circ - 244^\circ = 116^\circ$.

Step3: Compare the arc measures

We have $m\widehat{AC}=116^\circ$, $m\widehat{BC}=118^\circ$, $m\widehat{AB}=126^\circ$. So, $116^\circ<118^\circ<126^\circ$, which means $m\widehat{AC}

Answer:

$m\widehat{AC}$ < $m\widehat{BC}$ < $m\widehat{AB}$