Inscribed Angles and Arcs

This video tutorial by Mr. Backberg explores inscribed angles within circles. It explains that an inscribed angle has its vertex on the circle's edge and its sides as chords. The video details the relationship between the measure of an inscribed angle and the arc it intercepts, stating that the angle is half the arc's measure. Examples are provided to illustrate this concept, and the video also introduces the property that inscribed angles intercepting the same arc are congruent.

What is the defining characteristic of an inscribed angle in a circle?

• Its vertex is on the outer edge of the circle.

• Its vertex is at the center of the circle.

• It is always an obtuse angle.

• It is always a right angle.

Which of the following statements is true about the sides of an inscribed angle?

• They are radii of the circle.

• They are diameters of the circle.

• They are tangents to the circle.

• They are chords of the circle.

How is the measure of an inscribed angle related to the arc it intercepts?

• It is twice the arc's measure.

• It is half the arc's measure.

• It is one-third the arc's measure.

• It is equal to the arc's measure.

If an inscribed angle measures 30°, what is the measure of the arc it intercepts?

• 90°

• 60°

• 30°

• 15°

If an inscribed angle measures 45°, what is the measure of the arc it intercepts?

• 45°

• 180°

• 90°

• 135°

If an inscribed angle measures 20°, what is the measure of the arc it intercepts?

• 20°

• 40°

• 60°

• 80°

If an inscribed angle measures 35°, what is the measure of the arc it intercepts?

• 140°

• 35°

• 70°

• 105°

If an inscribed angle measures 15°, what is the measure of the arc it intercepts?

• 45°

• 15°

• 30°

• 60°

Given an arc measure of 84°, what is the measure of the inscribed angle that intercepts it?

• 63°

• 42°

• 84°

• 21°

What is the measure of an inscribed angle if the arc it intercepts measures 100°?

• 50°

• 100°

• 25°

• 75°