Central Angles and Arcs

This video tutorial explains central angles in a circle, defining them as angles with vertices at the circle's center and sides as radii. It highlights that the degree of a central angle is equal to its corresponding arc. The video provides examples, showing how to calculate angles and arcs, including solving equations with variables. It concludes with a call to action for viewers to engage with the content.

What is a central angle in a circle?

• An angle that divides the circle into two equal parts

• An angle that is always 90 degrees

• An angle whose vertex is at the center of the circle

• An angle whose vertex is on the circumference

If a central angle measures 50 degrees, what is the measure of its corresponding arc?

• 25 degrees

• 360 degrees

• 50 degrees

• 100 degrees

In a circle, if the arc measures 30 degrees, what is the measure of the central angle?

• 60 degrees

• 15 degrees

• 30 degrees

• 90 degrees

If the arc of a circle is 65 degrees, what is the measure of the major arc?

• 180 degrees

• 295 degrees

• 65 degrees

• 360 degrees

Given a central angle of 2x and an arc of 28 degrees, what is the value of x?

• 56

• 28

• 14

• 7

If a central angle is 88 degrees and the arc is represented by 10x - 2, what is x?

• 11

• 10

• 9

• 8

What is the total degree measure of a circle?

• 450 degrees

• 360 degrees

• 180 degrees

• 270 degrees

If a circle is divided into two arcs by a central angle, what is the sum of the measures of these arcs?

• 450 degrees

• 360 degrees

• 270 degrees

• 180 degrees

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

• The central angle is unrelated to the arc

• The central angle is always half of the arc

• The central angle is always double the arc

• The central angle and the arc have the same measure

What should you do if you have questions about central angles?

• Ignore them

• Search online

• Ask a friend

• Leave a comment on the video