Inscribed Angles and Intercepted Arcs

This video tutorial covers the concept of inscribed angles in geometry, explaining their properties and how they relate to intercepted arcs. It discusses the conditions under which inscribed angles are congruent and provides examples to illustrate these concepts. The tutorial also includes problem-solving exercises that involve calculating angle measures and solving for variables using algebraic expressions.

What is an inscribed angle?

• An angle with its vertex on the circle and sides that are radii

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

• An angle with its vertex on the circle and sides that are chords

• An angle with its vertex outside the circle

Which of the following is true about a central angle?

• Its vertex is on the circle

• Its vertex is at the center of the circle

• Its sides are tangents to the circle

• Its sides are secants of the circle

What is an intercepted arc?

• An arc that lies between the endpoints of an inscribed angle

• An arc that lies between the endpoints of a diameter

• An arc that is equal to the circumference of the circle

• An arc that lies outside the circle

If the intercepted arc of an inscribed angle measures 60 degrees, what is the measure of the inscribed angle?

• 60 degrees

• 30 degrees

• 120 degrees

• 90 degrees

What happens when an inscribed angle intercepts a diameter?

• The angle becomes an acute angle

• The angle becomes a straight angle

• The angle becomes a right angle

• The angle becomes an obtuse angle

If an inscribed angle intercepts a diameter, what is the measure of the angle?

• 60 degrees

• 90 degrees

• 45 degrees

• 180 degrees

What is true about two inscribed angles that intercept the same arc?

• They are complementary

• They are supplementary

• They are equal to the central angle

• They are congruent

If two inscribed angles intercept the same arc, what can be said about their measures?

• One is half the other

• They are equal

• They are different

• One is double the other

If an inscribed angle measures 31 degrees, what is the measure of its intercepted arc?

• 31 degrees

• 62 degrees

• 15.5 degrees

• 93 degrees

If an inscribed angle measures 113 degrees, what is the measure of the major arc it intercepts?

• 113 degrees

• 226 degrees

• 339 degrees

• 452 degrees