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Warm Up

Use Inscribed Angles and Polygons. Warm Up. Lesson Presentation. Lesson Quiz. 25. ANSWER. 60º; 120º. ANSWER. Warm-Up. 1. The measure of the interior angles of a quadrilateral are 80º, 100º, 55º, and 5 x º . Find the value of x.

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Warm Up

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  1. Use Inscribed Angles and Polygons Warm Up Lesson Presentation Lesson Quiz

  2. 25 ANSWER 60º; 120º ANSWER Warm-Up 1.The measure of the interior angles of a quadrilateralare 80º, 100º, 55º, and 5xº. Find the value of x. 2.Two supplementary angles have measures 6xº and12xº. Find each angle measure.

  3. 3.Solve 3x = ( 4x + 12). 1 2 1 2 6 ANSWER 4. Solve 80 = ( 360 – 2x). 100 ANSWER Warm-Up

  4. Find the indicated measure inP. a. mT b. mQR a. M T = mRS = (48o) = 24o mTQ = 2m R = 2 50o = 100o.BecauseTQR is a semicircle, b. mQR = 180o mTQ = 180o 100o = 80o. So,mQR = 80o. – – 1 1 2 2 Example 1 SOLUTION

  5. Find mRSand mSTR. What do you notice about STRand RUS? From Theorem 10.7,you know thatmRS = 2m RUS= 2 (31o) = 62o. Also, m STR = mRS = (62o) = 31o. So,STR RUS. 1 1 2 2 Example 2 SOLUTION

  6. Notice thatJKM andJLM intercept the same arc, and soJKM JLM by Theorem 10.8. Also, KJL andKML intercept the same arc, so they must also be congruent. Only choice C contains both pairs of angles. So, by Theorem 10.8, the correct answer is C. Example 3 SOLUTION

  7. 1. ANSWER 45° Guided Practice Find the measure of the red arc or angle.

  8. 2. ANSWER 76° Guided Practice Find the measure of the red arc or angle.

  9. 3. ANSWER 72° Guided Practice Find the measure of the red arc or angle.

  10. Example 4 Photography Your camera has a 90° field of vision and you want to photograph the front of a statue. You move to a spot where the statue is the only thing captured in your picture, as shown. You want to change your position. Where else can you stand so that the statue is perfectly framed in this way?

  11. Example 4 SOLUTION From Theorem 10.9, you know that if a right triangle is inscribed in a circle, then the hypotenuse of the triangle is a diameter of the circle. So, draw the circle that has the front of the statue as a diameter. The statue fits perfectly within your camera’s 90o field of vision from any point on the semicircle in front of the statue.

  12. ANSWER Make the diameter of your circle the diagonal of the rectangular base. Guided Practice 4. WHAT IF? In Example 4,explain how to find locations if you want to frame the front and left side of the statue in your picture.

  13. a. PQRS is inscribed in a circle, so opposite angles are supplementary. a. mQ + m S = 180° m P + m R = 180° Example 5 Find the value of each variable. SOLUTION 75° + y° = 180° 80° + x° = 180° y = 105 x = 100

  14. b. JKLMis inscribed in a circle, so opposite angles are supplementary. b. mK + m M = 180° m J + m L = 180° Example 5 Find the value of each variable. SOLUTION 2a° + 2a° = 180° 4b° + 2b° = 180° 4a = 180 6b = 180 a = 45 b = 30

  15. 5. ANSWER x = 98, y = 112 Guided Practice Find the value of each variable.

  16. 6. ANSWER c = 62, x = 10 Guided Practice Find the value of each variable.

  17. 1. ANSWER ANSWER 38 56 Lesson Quiz Find the value of x . 2.

  18. ANSWER 44 Lesson Quiz Find the value of x . 3.

  19. ANSWER x = 54; y = 20 Lesson Quiz Find the value of each variable. 4.

  20. ANSWER x = 5; y = 10 Lesson Quiz Find the value of each variable. 5.

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