Angles and Arcs

1
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.

2
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.

3
Angles and Arcs

• Theorem 10.1
• 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.

4
Example 2-1e
Answer 65
Answer 40
5
Example 2-2g
Answer 54
Answer 72
Answer 234
6
Example 2-3e
7
Example 2-3f
Answer no
8
Example 2-4c