Question

inscribed angle ( abc ) is ( 35^{circ} ) and shares points ( a ) and ( c ) with central angle ( aoc ). what is the measure of ( angle aoc )? use the keypad to enter the answer in the box. include the correct symbol for the units of measure.

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of a central angle is twice the measure of an inscribed angle that subtends the same arc.

Step2: Apply the theorem

Given the inscribed angle \(\angle ABC = 35^{\circ}\), and the central angle \(\angle AOC\) subtends the same arc as \(\angle ABC\). Let \(m\angle AOC=\theta\) and \(m\angle ABC = \alpha\). By the inscribed - angle theorem \(\theta = 2\alpha\).
Substitute \(\alpha=35^{\circ}\) into the formula: \(\theta=2\times35^{\circ}\)

Answer:

\(70^{\circ}\)