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Geometry

Geometry. 9.6 Interior and Exterior Angles. Interior Angle Theorem. The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs. A. B. m<1 = ½ ( mAD + mBC ). 60˚. 1. 50˚. C. If mAD = 50 and mBC = 60.

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Geometry

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  1. Geometry 9.6 Interior and Exterior Angles

  2. Interior AngleTheorem The measure of an angle formed by two chords that intersect inside a circle is equal to half thesum of the measures of the intercepted arcs. A B m<1 = ½( mAD + mBC ) 60˚ 1 50˚ C If mAD = 50 and mBC = 60 D 55 m<1 = ½(50 + 60) = _____

  3. x 80 X O O 100 20 Let’s try some exercises! (which wonderful student can draw some pictures on the board?) 90 = ½(100 + x) Find the value of x. 50 80 x = _____ x = _____ 1. 2.

  4. 70 160 x 140 O O x 40 Try these! Be careful: Notice which angle x is Find the value of x. 120 125 x = _____ x = _____ 3. 4.

  5. Exterior Angle Theorem(this is not in your packet) The measure of the angles formed by intersecting secants and tangents outside a circle is equal to half thedifference of the measures of the intercepted arcs. x˚ y˚ 1 x˚ y˚ 3 y˚ 2 x˚ m<1 = ½(x – y) m<3 = ½(x – y) m<2 = ½(x – y)

  6. 230 150 O A O B x 35 x Let’s try some exercises! 130 35 = ½(150-x) Find the value of x. 50 80 x = _____ x = _____ 1. 2. Don’t forget about the ½

  7. 80 x 30 O O 140 120 100 x Let’s do these! 180 semicircle 50 Find the value of x. 30 10 x = _____ x = _____ 3. 4. Don’t forget about the ½

  8. 40 x 105 85 O O x Try the next four. 85 = ½(105 + x) 40 = ½[(360-x) – x] 40 = ½[360 – 2x] Find the value of x. 80 = 360 – 2x 2x = 280 65 x = _____ 1. 140 x = _____ 2.

  9. x 20 x 120 O O 160 55 More Problems 80 Find the value of x. 15 40 x = _____ x = _____ 3. 4.

  10. Find the measure of each numbered angle. We can put the screen up and write on the picture. D AB is a tangent 125 ● C 6 B mAG = 100 30 E mCE = 30 25 8 O 5 mEF = 25 3 A ● F 7 2 1 4 80 62.5 m<5 = ____ m<6 = ____ m<7 = ____ m<8 = ____ m<1 = ____ m<2 = ____ m<3 = ____ m<4 = ____ 80 100 100 35 G 27.5 90 117.5 62.5

  11. Homework pg. 358 CE #1-9 WE # 1-23

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