Circle Geometry and Arc Measures

This video tutorial by Reggie covers the concepts of central angles and arcs in circles. It explains the relationships between angles and arcs, including the measure of a circle, semicircles, and vertical angles. The tutorial provides examples and problem-solving techniques, including algebraic methods, to find the measures of angles and arcs. The learning objectives include understanding the relation among arcs and central angles, finding their measures, and applying accumulated knowledge for new understanding.

What is the total degree measure of a full circle?

• 270 degrees

• 180 degrees

• 90 degrees

• 360 degrees

What is the degree measure of a semicircle?

• 90 degrees

• 270 degrees

• 180 degrees

• 360 degrees

Which of the following is true about vertical angles?

• They are always complementary

• They are always different

• They are always equal

• They are always supplementary

Where is the vertex of a central angle located?

• Anywhere inside the circle

• On the circumference

• Outside the circle

• At the center of the circle

If a central angle measures 65 degrees, what is the measure of its intercepted arc?

• 360 degrees

• 180 degrees

• 65 degrees

• 130 degrees

In a circle, if the measure of angle XYZ is 68 degrees, what is the measure of the minor arc XE?

• 68 degrees

• 112 degrees

• 292 degrees

• 180 degrees

If segment AB is a diameter and angle AQB is 96 degrees, what is the measure of arc AB?

• 84 degrees

• 96 degrees

• 180 degrees

• 360 degrees

How do you find the measure of a major arc if you know the measure of the minor arc?

• Add 180 degrees

• Subtract from 360 degrees

• Divide by 2

• Double the minor arc

If the measure of arc AL is 100 degrees, what is the measure of the major arc ACL?

• 360 degrees

• 100 degrees

• 260 degrees

• 160 degrees

In circle C, if arc TK is 30 degrees, what is the measure of the central angle ECA?

• 60 degrees

• 120 degrees

• 30 degrees

• 90 degrees