1. 10-2 Measuring Angles and Arcs
You measured angles and identified congruent angles.
Identify central angles, major arcs, minor arcs, and semicircles, and find their measures.
Find arc lengths.

2. Central angles
Central angles are angles whose vertices are at the center of the circle.
Central angle
p. 706

3. Find Measures of Central Angles
Find the value of x.
The sum of the measures of
Substitution
Simplify.
Add 2 to each side.
Divide each side by 26.
Answer: x = 7

4. Arcs—parts of a circle
Minor arc AB
There are three kinds of arcs made by central angles:
Major arcs: greater than 180°
Named with 3 letters
Minor arcs: less than 180°
Named with 2 letters
Semi-circles: exactly 180°
one-half of a circle A C B D
Major arc ADB A B C D

5. Measures in Degrees Complete circle measures 360°.
The measure of any semicircle is 180°.
(½ of a circle)
360°
180° C A B

6. p. 707

7. Measures
Measure of a minor arc is equal to the measure of the central angle.
Measure of the major arc is equal to 360° minus the measure of its minor arc. W Y
80° X Z W
mXZY = 360°−mWX
80° Y X Z

8. Answer:

9. Answer:

10. Answer:

11. Definition
Congruent arcs are arcs in the same circle (or congruent circles) that have the same measure. A Y
60°
60° B X

12. p. 707

13. mLPK = 0.21(360) Find 21% of 360.
= 75.6 Simplify.
Answer:

14. Sum of arcs in a circle is 360.
Substitution
Simplify.
Simplify.
Answer:

15. A B C D

16. Find each arc measure in סּLQ L
54°
306°
180°
mMN
mMPN
mPQN
54° P

17. 10-2Assignment
Page 710, 12-24