Question

in the figure below, o is the center of the circle. find each measurement below. a. m∠aco b. mac c. mcb d. mab

Explanation:

Step1: Recall the property of inscribed - angle and central - angle

The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. Also, the sum of the measures of arcs in a circle is 360°.

Step2: Find the measure of arc \(AB\)

We know that the sum of the measures of arcs \(AC\), \(CB\), and \(AB\) is 360°. Given \(m\widehat{AC}=116^{\circ}\) and \(m\widehat{CB} = 64^{\circ}\).
Let \(m\widehat{AB}=x\). Then \(x+116 + 64=360\).

Step3: Solve the equation for \(x\)

\[

$$\begin{align*} x+180&=360\\ x&=360 - 180\\ x&=180 \end{align*}$$

\]

Answer:

\(180\)