1. 10.2 Finding Arc Measures

2. What We Will Learn
Find arc measure
Identify congruent arcs

3. Needed Vocab
Central angle: angle whose vertex is the center of the circle
Minor arc: less than 180 degrees; uses two letters
Major arc: greater than 180 degrees; uses three letters
Semicircle: half a circle
Measure of minor arc: measure of its related central angle
Measure of major arc: difference of 360 degrees and related minor arc
Adjacent arcs: two arcs that intersect at exactly one point
Congruent circles: two or more circles with the same radius
Congruent arcs: arcs whose central angles are congruent
Similar arcs: arcs with same measure

4. Ex. 1 Finding Measures of Arcs
Remember to read arcs in the order of the letters to see which arc they are talking about
Remember two letters is a minor arc and three letters is a major arc
A. arc RS
110°
B. arc RTS
250°
C. arc RST
180°

5. Ex. 2 Using Arc Addition Find each measure: A. arc GE 120° B. arc GEF
230°
C. arc GF
130°

6. Ex. 3 Finding Measures of Arcs
A recent survey asked teenagers whether they would rather meet a famous musician, athlete, actor, inventor, or other person. The circle graph shows the results. Find the indicated arc measures.
A. arc AC
137°
B. arc ACD
220°
C. arc ADC
223°
D. arc EBD
299°

7. Ex. 4 Identifying Congruent Arcs
Tell whether the red arcs are congruent. Explain
A. yes because same central angle of same circle
B. no because although same central angle not congruent circles
C. yes because same central angle and congruent circles because radius congruent