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Warm-Up Exercises Find x and y. 1. ANSWER x = 60; y = 60 2. ANSWER x = 35; y = 35 Warm-Up1Exercises EXAMPLE Find measures of arcs Find the measure of each arc of P, where RT is a diameter. a. RS b. RTS c. RST SOLUTION RPS = 110o. a. RS is a minor arc, so mRS = m b. RTS is a major arc, so mRTS = 360o – 110o = 250o. c. RT is a diameter, so RST is a semicircle, and mRST = 180o. Warm-Up2Exercises EXAMPLE Find measures of arcs Survey 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. a. mAC SOLUTION a. mAC = mAB + mBC = 29o + 108o = 137o Warm-Up2Exercises EXAMPLE Find measures of arcs Survey 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. b. mACD SOLUTION b. mACD = mAC + mCD = 137o + 83o = 220o Warm-Up2Exercises EXAMPLE Find measures of arcs Survey 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. c. mADC SOLUTION c. mADC = 360o – mAC = 360o – 137o = 223o Warm-Up2Exercises EXAMPLE Find measures of arcs Survey 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. d. mEBD SOLUTION d. mEBD = 360o – mED = 360o – 61o = 299o 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. Warm-Up Exercises GUIDED PRACTICE 1. for Examples 1 and 2 TQ SOLUTION TQ is a minor arc, so m TQ = 120o. 2. QRT SOLUTION QRT is a major arc, so m QRT= 240o. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 3. TQR SOLUTION TQR is a semicircle, so m TQR = 180o. 4. QS SOLUTION QS is a minor arc, so m QS = 160o. Warm-Up Exercises GUIDED PRACTICE 5. for Examples 1 and 2 TS SOLUTION TS is a minor arc, so m TS = 80o. 6. RST SOLUTION RST is a semicircle, so m RST = 180o. Warm-Up3Exercises EXAMPLE 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. Warm-Up3Exercises EXAMPLE 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 . Warm-Up Exercises 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 . 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. Daily Homework Quiz Warm-Up Exercises Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 1. BC ANSWER o minor arc, 32 Daily Homework Quiz Warm-Up Exercises Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 2. CBE ANSWER o major arc, 212 Daily Homework Quiz Warm-Up Exercises Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 3. BCE ANSWER o semicircle, 180 Daily Homework Quiz Warm-Up Exercises Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 4. ~ BC . Explain why AE = ANSWER m AFE = m BFC because the angles are ~ BFC.Then vertical angles, so AFE = arcs AE and BC are arcs that have the same measure in the same circle. By ~ BC . definition AE = Daily Homework Quiz Warm-Up Exercises 5. o . AD Two diameters of P are AB and CD.If m = 50 , find m ACD and m AC . ANSWER o o 310 ; 130