Angles and Arc Relationships

The video tutorial explains circumscribed angles, which are angles whose sides are tangent to a circle. It demonstrates how to find the measure of a circumscribed angle by subtracting the central angle from 180 degrees. The tutorial includes three examples: calculating a circumscribed angle, using the inscribed angle theorem, and applying trigonometry to solve for angles. Each example illustrates different methods and theorems to find angle measures in geometric figures involving circles.

What is a circumscribed angle?

• An angle that is equal to the central angle

• An angle inside a circle

• An angle whose sides are tangent to a circle

• An angle formed by two chords

How do you find the measure of a circumscribed angle?

• Multiply the central angle by 2

• Add 90 degrees to the central angle

• Divide the central angle by 2

• Subtract the central angle from 180 degrees

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

• The central angle is double the arc

• The central angle is equal to the arc

• The central angle is unrelated to the arc

• The central angle is half the arc

In Example 1, if the central angle is 124 degrees, what is the circumscribed angle?

• 90 degrees

• 180 degrees

• 124 degrees

• 56 degrees

In Example 2, if the circumscribed angle is 42 degrees, what is the central angle?

• 138 degrees

• 90 degrees

• 180 degrees

• 42 degrees

What theorem is used to find the measure of an inscribed angle?

• Chord Theorem

• Inscribed Angle Theorem

• Central Angle Theorem

• Tangent-Secant Theorem

In Example 2, what is the measure of arc BC if the central angle is 138 degrees?

• 69 degrees

• 138 degrees

• 180 degrees

• 42 degrees

What is the measure of an inscribed angle if its intercepted arc is 138 degrees?

• 69 degrees

• 138 degrees

• 180 degrees

• 42 degrees

What is the measure of angle E if arc BC is 138 degrees?

• 138 degrees

• 69 degrees

• 180 degrees

• 42 degrees

What is the measure of angle BAC if the circumscribed angle is 42 degrees?

• 138 degrees

• 42 degrees

• 90 degrees

• 180 degrees