Given a circle with points $O$, $A$, and $C$ on its circumference, and major arc $AB$ measures $220°$, what is the measure of angle $\angle OAC$?

• A. $70°$
• B. $55°$
• C. $110°$
• D. $140°$

Answer: (C)

Verified step by step guidance

1. Identify the given information: the major arc \( AB \) measures \( 220^\circ \). Since the circle's total circumference is \( 360^\circ \), find the measure of the minor arc \( AB \) by subtracting the major arc from \( 360^\circ \).
2. Recall that the angle \( \angle OAC \) is an inscribed angle that intercepts arc \( OC \) or arc \( BC \) depending on the points' arrangement. Determine which arc \( \angle OAC \) intercepts based on the problem's description.
3. Use the Inscribed Angle Theorem, which states that an inscribed angle is half the measure of its intercepted arc. Express \( \angle OAC \) as half the measure of the intercepted arc.
4. Calculate the intercepted arc's measure using the information about the major arc \( AB \) and the circle's total degrees, then apply the Inscribed Angle Theorem to find \( \angle OAC \).
5. Conclude by writing the measure of \( \angle OAC \) as \( \frac{1}{2} \times \text{(intercepted arc measure)} \), which leads to the final angle measure.