Find Measures of Inscribed Angles Using Central Angles

This video tutorial explains the central angle theorem, which states that the measure of an inscribed angle is half of the measure of the central angle. It covers three cases of the theorem, demonstrating how to calculate inscribed angles using isosceles triangles and supplementary angles. The video also clarifies the difference between arc major and arc length, and concludes with an example calculation of an inscribed angle from a given central angle.

What is a common misconception about arc major and arc length?

• Arc major is the same as arc length.

• They are both measures of distance.

• Arc major is always larger than arc length.

• They are both measures of angles.

In the first case of the central angle theorem, what is the relationship between the inscribed angle and the central angle?

• The inscribed angle is twice the central angle.

• The inscribed angle is half the central angle.

• The inscribed angle is equal to the central angle.

• The inscribed angle is unrelated to the central angle.

What type of triangle is used to demonstrate the first case of the central angle theorem?

• Isosceles triangle

• Scalene triangle

• Right triangle

• Equilateral triangle

In the second case of the central angle theorem, what is the position of the center relative to the inscribed angle?

• On the side of the inscribed angle

• At the vertex of the inscribed angle

• Outside the circle

• Inside the inscribed angle

What is the relationship between the inscribed angle and the central angle in the second case?

• The inscribed angle is equal to the central angle.

• The inscribed angle is half the central angle.

• The inscribed angle is twice the central angle.

• The inscribed angle is unrelated to the central angle.

In the third case of the central angle theorem, what happens to the inscribed angle vertex?

• It moves inside the circle.

• It remains at the center.

• It moves on the circle.

• It moves outside the circle.

What is the measure of an inscribed angle if the intercepted arc measures 150 degrees?

• 300 degrees

• 150 degrees

• 75 degrees

• 100 degrees