Angles and Arcs

Central Angles –

An angle in a circle that has the center as its vertex and two radii as its sides.

Sum of Central Angles –

The sum of the measures of the central angles of a circle with no interior points in common is 360 degrees.

Angles and Arcs

Arc –

A collection of the points that make up a circle. The measure of an arc is related to the measure of its central angle.

Minor Arc –

An arc that is less than half of the circle. Its degree measure is equal to the measure of its central angle. It is named using the endpoints of the arc.

Major Arc –

An arc that is more than half of the circle. Its degree measure is equal to 360 minus the measure of its minor arc. It is named using the endpoints of the arc and a point between them.

Semicircle –

An arc that is half of the circle. Its degree measure is equal to 180. It is named using the endpoints and a point between them.

Theorem 10.1

Angles and Arcs

• In the same or congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent.

Arc Addition Postulate

• The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Arc Length

• The length of an arc is (m/360) times the circumference of the circle, where m is the measure of the corresponding central angle.

ALGEBRA Refer to .

a.

Find

m

Answer:

65

b.

Find

m

Answer:

40

In and are diameters, and bisects Find each measure.

a. Answer:

54

b.

Answer:

72

c. Answer:

234

SPEED LIMITS This graph shows the percent of U.S. states that have each speed limit on their interstate highways.

a.

Find the measurement of the central angles representing each category. List them from least to greatest.

Answer: b.

Is the arc for the wedge for 65 mph congruent to the combined arcs for the wedges for 55 mph and 70 mph?

Answer:

no

In and . Find the length of . Answer:

units or about 49.48 units