Angles and Arc Lengths in Circles

This video tutorial covers the measurement of angles and arcs in circles. It begins with an introduction to central angles, explaining that the sum of central angles in a circle is always 360 degrees. The tutorial then demonstrates how to find specific angle measures using given values and properties of vertical angles. It also explains the different types of arcs—minor, major, and semicircle—and how to name them. Finally, the video provides a formula for calculating arc lengths and demonstrates its application through examples.

What is the sum of all central angles in a circle?

• 90 degrees

• 270 degrees

• 360 degrees

• 180 degrees

If angle 1 is 120 degrees and angle 2 is 100 degrees, what is angle 3 in a circle?

• 140 degrees

• 140 degrees

• 140 degrees

• 120 degrees

What is the sum of angles in a triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

In a circle, if angle AOD is 25X, angle BOC is 3X, and angle COD is 2X, what is X if the sum of these angles is 180 degrees?

• 3

• 5

• 6

• 4

If angle AOD is 25X and X is 6, what is the measure of angle AOD?

• 120 degrees

• 180 degrees

• 90 degrees

• 150 degrees

What is the measure of angle AOE if it is 5X and X is 6?

• 120 degrees

• 90 degrees

• 60 degrees

• 30 degrees

What is a vertical angle?

• An angle that is 90 degrees

• An angle that is more than 180 degrees

• An angle that is congruent to its opposite

• An angle that is less than 90 degrees

What is a minor arc?

• An arc more than 180 degrees

• An arc exactly 180 degrees

• An arc that is a full circle

• An arc less than 180 degrees

How do you name a major arc?

• With two letters

• With three letters

• With one letter

• With four letters

What is a semicircle?

• An arc more than 180 degrees

• An arc exactly 180 degrees

• An arc less than 180 degrees

• An arc that is a full circle