Interior and Exterior Angle Theorems

The video tutorial covers the use of interior and exterior angle theorems in circles. It begins with an introduction to these concepts, followed by detailed examples demonstrating how to apply the theorems to solve for angles and arcs. The tutorial includes both straightforward and complex problems, emphasizing the importance of algebraic manipulation and verification of results. The session concludes with encouragement for students to practice independently.

What section of the textbook is referenced for additional examples on interior and exterior angles?

• Section 10.6

• Section 9.4

• Section 12.1

• Section 11.2

According to the interior angle theorem, the angle measure is equal to half of what?

• The product of the two arcs

• The sum of the two arcs

• The square of the two arcs

• The difference of the two arcs

In the first example, what is the calculated angle measure when the arcs are 74 and 22 degrees?

• 96 degrees

• 74 degrees

• 52 degrees

• 48 degrees

In the second example, if the angle is 80 degrees and one arc is 45 degrees, what is the other arc?

• 90 degrees

• 135 degrees

• 115 degrees

• 100 degrees

What is the key difference in approach between the interior and exterior angle theorems?

• Squaring arcs vs. taking square roots

• None of the above

• Adding arcs vs. subtracting arcs

• Multiplying arcs vs. dividing arcs

In the exterior angle theorem, what must the arcs add up to in a circle?

• 180 degrees

• 270 degrees

• 360 degrees

• 90 degrees

What is the calculated angle when the big arc is 135 degrees and the small arc is 20 degrees?

• 60 degrees

• 55 degrees

• 50 degrees

• 57.5 degrees

In the variation with two tangents, what is the big arc if the small arc is 132 degrees?

• 228 degrees

• 132 degrees

• 360 degrees

• 180 degrees

In the example with a tangent and a secant, what is the arc measure if the angle is 40 degrees and the big arc is 130 degrees?

• 60 degrees

• 50 degrees

• 40 degrees

• 70 degrees

What type of angle is formed when the vertex is on the circle?

• Interior angle

• Exterior angle

• Inscribed angle

• Central angle