Understanding Angles in a Circle

The video tutorial explains how to find the measure of angles within a circle that are not at the center, referred to as nomatic angles. It introduces the concept of intercepted arcs and vertical angles, and explains the bow tie rule, which involves averaging the measures of intercepted arcs to find the angle measure. An example calculation is provided, demonstrating the process of adding and dividing by two. The tutorial also touches on supplementary angles and their properties.

What is a 'nomatic angle' in the context of circle geometry?

• An angle that forms a right angle

• An angle inside the circle but not at the center

• An angle outside the circle

• An angle at the center of the circle

Tags

CCSS.HSF.TF.A.1

How do you find the measure of an angle inside a circle?

• By using the diameter

• By measuring the radius

• By calculating the circumference

• By averaging the intercepted arcs

Tags

CCSS.HSG.C.A.2

What is the first step in finding the measure of an angle using intercepted arcs?

• Subtract the arcs

• Divide the arcs

• Multiply the arcs

• Add the arcs

Tags

CCSS.HSG.C.A.2

What does the 'bow tie' rule help determine?

• The diameter of the circle

• The length of the radius

• The congruence of vertical angles

• The area of the circle

Tags

CCSS.HSG.SRT.C.8

In the 'bow tie' rule, what do the two arcs intercepted by the vertical angles represent?

• The product of the angles

• The sum of the angles

• The average of the angles

• The difference of the angles

Tags

CCSS.HSG.CO.C.9

What is the relationship between vertical angles in the 'bow tie' rule?

• They are supplementary

• They are congruent

• They are complementary

• They are equal to the intercepted arcs

Tags

CCSS.HSG.C.A.2

If one intercepted arc is 100 degrees and another is 120 degrees, what is the measure of the angle inside the circle?

• 110 degrees

• 100 degrees

• 90 degrees

• 120 degrees

Tags

CCSS.HSG.C.A.2

What is the result of dividing the sum of two intercepted arcs by two?

• The measure of the supplementary angle

• The measure of the angle inside the circle

• The measure of the central angle

• The measure of the external angle

Tags

CCSS.7.G.B.5

What is the sum of the measures of supplementary angles?

• 270 degrees

• 90 degrees

• 360 degrees

• 180 degrees

Tags

CCSS.7.G.B.5

If an angle is 110 degrees, what is the measure of its supplementary angle?

• 110 degrees

• 90 degrees

• 70 degrees

• 180 degrees

Tags

CCSS.7.G.B.5