How to find the measure of an angle using inscribed angles

The video tutorial covers the concepts of central and inscribed angles in geometry. It explains that a central angle has its vertex at the center of a circle, and its measure is equal to the arc it intercepts. In contrast, an inscribed angle has its vertex on the circle, and its measure is half of the intercepted arc. The tutorial includes examples to illustrate these concepts, showing how to calculate arc measures for both types of angles.

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

• The central angle is unrelated to the arc measure.

• The central angle is equal to the arc measure.

• The central angle is half the arc measure.

• The central angle is twice the arc measure.

Where is the vertex of an inscribed angle located?

• At the center of the circle

• On the circle

• Outside the circle

• Inside the circle but not at the center

How does the measure of an inscribed angle compare to its arc?

• It is half the arc measure.

• It is twice the arc measure.

• It is unrelated to the arc measure.

• It is equal to the arc measure.

If an inscribed angle measures 30 degrees, what is the measure of its arc?

• 30 degrees

• 15 degrees

• 60 degrees

• 90 degrees

Given an arc measure of 162 degrees, what is the measure of the inscribed angle?

• 162 degrees

• 81 degrees

• 54 degrees

• 108 degrees