Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is true about an inscribed angle?

1. The arc measurement is half the angle measurement

2. The angle measurement is double the arc measurement

3. The angle is always obtuse

4. The inscribed angle is equal to the central angle

The correct answer is: The arc measurement is half the angle measurement

An inscribed angle is defined as an angle formed by two chords in a circle which have a common endpoint. This angle opens to an arc on the circle, and the relationship between the inscribed angle and the measure of the arc it intercepts is a fundamental property in circle geometry. Specifically, the measure of the inscribed angle is precisely half the measure of the intercepted arc. This relationship arises from the way the central angle subtended by the same arc directly correlates to the inscribed angle. In contrast, the other statements do not accurately describe the characteristics of inscribed angles: the notion that the angle measurement is double the arc measurement misrepresents the fundamental relationship; stating that the angle is always obtuse does not hold true as inscribed angles can also be acute or right; and claiming that the inscribed angle equals the central angle contradicts the established fact that the central angle is actually double the inscribed angle’s measurement. Understanding this property can significantly enhance one's grasp of circle-related problems in geometry.