Question

in circle o, m\\(widehat{ac}\\) = m\\(widehat{bc}\\) = 160. what is m\\(\angle aob\\)? (not drawn to scale) a 20 b 80 c 40 d 200

Explanation:

Step1: Recall circle - arc relationship

The sum of the measures of the arcs of a circle is 360°.

Step2: Calculate sum of given arcs

$m\overparen{AC}+m\overparen{BC}=160 + 160=320$.

Step3: Find measure of $\overparen{AB}$

$m\overparen{AB}=360-(m\overparen{AC}+m\overparen{BC})=360 - 320 = 40$.

Step4: Determine central - angle measure

The measure of a central angle is equal to the measure of its intercepted arc. So $m\angle AOB=m\overparen{AB}=40$.

Answer:

C. 40