Question

in the diagram, point o is the center of the circle. if m∠abc = 70°, what is m∠aoc?
a. 100°
b. 110°
c. 140°
d. 180°

Explanation:

Step1: Recall the central angle theorem

The central angle theorem states that the measure of a central angle ($\angle AOC$) is twice the measure of an inscribed angle ($\angle ABC$) that subtends the same arc ($\overset{\frown}{AC}$).

Step2: Apply the formula

Given $m\angle ABC = 70^{\circ}$, using the formula $m\angle AOC=2\times m\angle ABC$.
Substitute the value: $m\angle AOC = 2\times70^{\circ}$.

Answer:

$140^{\circ}$ (Option C)