1. Warm-Up Exercises ANSWER x = 60; y = 60 ANSWER x = 35; y = 35 1. Find x and y. 2.

2. Warm-Up Exercises EXAMPLE 1 Find measures of arcs RS a. RTS b. RST c. SOLUTION RS is a minor arc, so mRS = m RPS = 110 o. a. RTS is a major arc, so mRTS = 360 o 110 o = 250 o. b. – Find the measure of each arc of P, where RT is a diameter. c. RT is a diameter, so RST is a semicircle, and mRST = 180 o.

3. Warm-Up Exercises EXAMPLE 2 Find measures of arcs A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey a. mAC SOLUTION a. mAC mAB =+ mBC = 29 o + 108 o = 137 o

4. Warm-Up Exercises EXAMPLE 2 Find measures of arcs b. mACD = mAC + mCD = 137 o + 83 o = 220 o A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey SOLUTION b. mACD

5. Warm-Up Exercises EXAMPLE 2 Find measures of arcs mADC mAC = 360 o – c. = 360 o – 137 o = 223 o A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey SOLUTION c. mADC

6. Warm-Up Exercises EXAMPLE 2 Find measures of arcs d. mEBD = 360 o – mED = 360 o – 61 o = 299 o d. mEBD A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey SOLUTION

7. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Identify the given arc as a major arc, minor arc, or semicircle, and find the measure of the arc.

8. Warm-Up Exercises TQ is a minor arc, so m TQ = 120 o. GUIDED PRACTICE for Examples 1 and 2 1. TQ SOLUTION. QRT2 SOLUTION QRT is a major arc, so m QRT= 240 o.

9. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2. TQR3 SOLUTION TQR is a semicircle, so m TQR = 180 o.. QS4 SOLUTION QS is a minor arc, so m QS = 160 o.

10. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2. TS5 SOLUTION TS is a minor arc, so m TS = 80 o.. RST6 SOLUTION RST is a semicircle, so m RST = 180 o.

11. Warm-Up Exercises EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. a. b. SOLUTION a. CD EF because they are in the same circle and mCD = mEF b. RS and TU have the same measure, but are not congruent because they are arcs of circles that are not congruent.

12. Warm-Up Exercises c. VX YZ because they are in congruent circles and mVX = mYZ. EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. c. SOLUTION

13. Warm-Up Exercises GUIDED PRACTICE for Example 3 Tell whether the red arcs are congruent. Explain why or why not. 7. AB CD because they are in congruent circles and mAB = mCD. SOLUTION

14. Warm-Up Exercises GUIDED PRACTICE for Example 3 Tell whether the red arcs are congruent. Explain why or why not. 8. SOLUTION MN and PQ have the same measure, but are not congruent because they are arcs of circles that are not congruent.

15. Warm-Up Exercises Daily Homework Quiz Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 1. BC ANSWERminor arc, 32 o

16. Warm-Up Exercises Daily Homework Quiz 2. Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. CBE ANSWERmajor arc, 212 o

17. Warm-Up Exercises Daily Homework Quiz 3. Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. BCE ANSWERsemicircle, 180 o

18. Warm-Up Exercises Daily Homework Quiz 4. Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. BC AE Explain why = ~. ANSWER BC AE = ~ m AFE = m BFC because the angles are vertical angles, so AFE BFC.Then arcs and are arcs that have the same measure in the same circle. By definition. = ~ AE BC

19. Warm-Up Exercises Daily Homework Quiz 5. ACD AC Two diameters of P are AB and CD. If m = 50, find m and m.. AD o ANSWER o 310 ; 130 o