Angle Measures in Circles

This lesson covers the concepts of secants, tangents, and angle measures in circles. It explains how to find the measures of angles formed by lines intersecting on, inside, or outside a circle. The lesson introduces the vocabulary of secants and tangents, and provides formulas for calculating angles based on arc measures. Example problems are solved to illustrate these concepts, emphasizing the importance of using the correct arc measures for accurate calculations.

What are the main objectives of this lesson on secants, tangents, and angle measures?

• To learn about the history of geometry

• To find measures of angles formed by lines intersecting circles

• To understand the properties of triangles

• To explore the concept of parallel lines

How many times does a secant intersect a circle?

• Once

• Not at all

• Twice

• Three times

What is the difference between a secant and a tangent?

• A secant intersects a circle once, a tangent twice

• A tangent intersects a circle once, a secant twice

• Both intersect a circle once

• Both intersect a circle twice

When lines intersect inside a circle, how is the angle measure determined?

• Half the sum of the arcs

• The full difference of the arcs

• Half the difference of the arcs

• The full sum of the arcs

What is the angle measure when the intersection is on the circle?

• Half the difference of the arcs

• Half of the one arc it opens up to

• Half the sum of the arcs

• The full sum of the arcs

How is the angle measure determined when the intersection is outside the circle?

• The full difference of the arcs

• The full sum of the arcs

• Half the difference of the arcs

• Half the sum of the arcs

In the example with intersection inside the circle, what is the measure of angle one?

• 202°

• 101°

• 180°

• 79°

What is the sum of the arcs used to find the measure of angle one in the example?

• 146

• 101

• 56

• 202

In the example with intersection on the circle, what is the measure of angle two?

• 226°

• 134°

• 113°

• 360°

What is the missing arc measure needed to find angle two in the example?

• 360°

• 226°

• 134°

• 101°