Question

find the arc measure of $widehat{ce}$. for 2 - 3, use circle c. 2. find $mwidehat{wx}$ 3. find $mwidehat{xz}$

Explanation:

Step1: Recall inscribed - angle theorem

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

Step2: Solve for problem 1

Let the inscribed angle be $43^{\circ}$. By the inscribed - angle theorem, if $m\angle = 43^{\circ}$, then $m\overset{\frown}{CE}=2\times m\angle$. So $m\overset{\frown}{CE}=2\times43 = 86^{\circ}$.

Step3: Solve for problem 2

The central angle is equal to the measure of the intercepted arc. If the central angle corresponding to $\overset{\frown}{WX}$ is $9^{\circ}$, then $m\overset{\frown}{WX}=9^{\circ}$.

Step4: Solve for problem 3

The sum of the measures of the arcs of a circle is $360^{\circ}$. Let $m\overset{\frown}{XZ}=x$. We know that there is a $106^{\circ}$ arc and a $9^{\circ}$ arc. So $x + 106+9=360$. Then $x=360-(106 + 9)=245^{\circ}$.

Answer:

1. $m\overset{\frown}{CE}=86^{\circ}$
2. $m\overset{\frown}{WX}=9^{\circ}$
3. $m\overset{\frown}{XZ}=245^{\circ}$