Understanding Central and Inscribed Angles

The video tutorial covers the concepts of central and inscribed angles in geometry. It begins by explaining central angles, where the vertex is at the center of the circle, and the arc's measure equals the angle's measure. The tutorial then transitions to inscribed angles, which have the vertex on the circle. The measure of an inscribed angle is half the measure of its intercepted arc. Examples are provided to illustrate these concepts, including calculations to demonstrate the relationship between the arc and the inscribed angle.

What is a central angle?

• An angle with no relation to a circle

• An angle with its vertex outside the circle

• An angle with its vertex at the center of the circle

• An angle with its vertex on the circle

What is the relationship between a central angle and its intercepted arc?

• The arc is twice the central angle

• The arc is equal to the central angle

• The arc is half the central angle

• The arc is unrelated to the central angle

How does an inscribed angle differ from a central angle?

• The inscribed angle has its vertex at the center

• The inscribed angle has its vertex on the circle

• The inscribed angle has no endpoints

• The inscribed angle is outside the circle

What is the measure of an inscribed angle compared to its intercepted arc?

• It is equal to the arc

• It is unrelated to the arc

• It is twice the arc

• It is half the arc

If the arc measures 70 degrees, what is the measure of the inscribed angle?

• 35 degrees

• 140 degrees

• Cannot be determined

• 70 degrees