Circle Angle Relationships and Arc Measures

The video tutorial explains homework from lesson 6, focusing on circle geometry. It covers various types of angles, including those inside and outside the circle, and provides step-by-step solutions to questions involving angle calculations using the sum and difference of arcs. The tutorial also includes algebraic solutions for more complex problems.

What is the rule for finding the measure of an angle inside a circle that is not central or inscribed?

• The angle is equal to the arc it intercepts.

• The angle is equal to half the sum of the arcs on either side.

• The angle is equal to the difference of the arcs on either side.

• The angle is equal to twice the arc it intercepts.

In question 1, if the arcs on either side of angle yzv are 144 and 114, what is the measure of angle yzv?

• 114

• 129

• 258

• 144

How do you solve for an unknown arc when given an angle inside the circle?

• Subtract the known arc from the angle and multiply by 2.

• Multiply the angle by 2 and add the known arc.

• Add the known arc to the angle and divide by 2.

• Multiply the angle by 2 and subtract the known arc.

In question 2, if the angle is 93 and one arc is 161, what is the value of the unknown arc?

• 25

• 161

• 93

• 186

What is the rule for an angle that appears inscribed but is not?

• The angle is equal to the sum of the arcs on either side.

• The angle is equal to the arc it intercepts.

• The angle is equal to half the arc it intercepts.

• The angle is equal to twice the arc it intercepts.

In question 3, if angle PQS is 128 degrees, what is the measure of the arc it intercepts?

• 256

• 104

• 128

• 360

What is the rule for finding the measure of an angle outside the circle?

• The angle is equal to the arc it intercepts.

• The angle is equal to half the sum of the arcs on either side.

• The angle is equal to twice the arc it intercepts.

• The angle is equal to half the difference of the arcs between its sides.

In question 4, if the arcs are 121 and 39, what is the measure of angle EFG?

• 41

• 121

• 39

• 82

How do you find an unknown arc when given an angle outside the circle?

• Multiply the angle by 2 and add the known arc.

• Subtract the known arc from the angle and divide by 2.

• Multiply the angle by 2 and subtract the known arc.

• Add the angle to the known arc and multiply by 2.

In question 5, if angle DEF is 53 degrees and one arc is 41, what is the value of the unknown arc CF?

• 41

• 53

• 147

• 106