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

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 = 29o + 108o = 137o

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 b. mACD SOLUTION b. mACD = mAC + mCD = 137o + 83o = 220o

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 c. mADC SOLUTION mADC mAC = 360o – c. = 360o – 137o = 223o

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 d. mEBD SOLUTION d. mEBD = 360o – mED = 360o – 61o = 299o

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.

GUIDED PRACTICE for Examples 1 and 2 1 . TQ SOLUTION TQ is a minor arc, so m TQ = 120o. . QRT 2 SOLUTION QRT is a major arc, so m QRT= 240o.

GUIDED PRACTICE for Examples 1 and 2 . TQR 3 SOLUTION TQR is a semicircle, so m TQR = 180o. . QS 4 SOLUTION QS is a minor arc, so m QS = 160o.

GUIDED PRACTICE for Examples 1 and 2 . TS 5 SOLUTION TS is a minor arc, so m TS = 80o. . RST 6 SOLUTION RST is a semicircle, so m RST = 180o.

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.

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

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

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.

Daily Homework Quiz Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 1. BC ANSWER minor arc, 32 o

Daily Homework Quiz Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 2. CBE ANSWER major arc, 212 o

Daily Homework Quiz Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 3. BCE ANSWER semicircle, 180 o

Daily Homework Quiz Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 4. Explain why AE = ~ BC . 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 .

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