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Bellwork One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle Solve for x 2x 2 -13x-7=0 Clickers

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Bellwork Solution One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle Solve for x 2x 2 -13x-7=0

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Section 10.5

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The Concept For the bulk of this chapter we’ve been dealing with the arc of circles Today we’re going to finish out our discussion of arcs and angles

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Theorem Theorem 10.11 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc A C B D This makes sense if we think about this in terms of an inscribed angle with only one leg

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On your own What is the measure of arc ADC 82 o A C B D

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On your own What is the measure of arc ABC 82 o A C B D

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On your own What is the measure of angle ACB, if arc CD measures 160 o 35 o A C B D

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Theorems Theorem 10.12 If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle A B C D x

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Example Find the measure of angle AEC A B C D E 110 o 96 o

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On your own What is the measure of angle ABC 225 o A C B D E 255 o

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On your own What is the measure of angle ABD 148 o A C B D E 30 o

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On your own What is the measure of arc AC 121 o A C B D E 142 o

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Theorems Theorem 10.13 Angles Outside the Circle Theorem If a tangent and a secant, two tangents or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs A B C D

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Theorems Find the measure of angle ADB A B D 250 o 110 o C

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On your own What is the measure of angle ABD 30 o A C B D E 86 o

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On your own What is the measure of angle ADB 65 o A B D 195 o

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On your own What is the measure of arc BD 32 o A B D 164 o

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On your own What is the measure of arc AB 22 o A B D 120 o

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On your own What is the measure of angle of E, if arc ABC is 200 o A B D C E

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On your own What is the measure of angle of F? A B D C F 110 o 80 o

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On your own What is the measure of angle of F? A B D C F 35 o 110 o 105 o

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Homework 10.5 1-20, 22-25

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Most Important Points Angle-Chord Relationships that intercept inside a circle Angle relationship that intersects outside the circle

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10.4: Angles formed by Secants and Tangents Obj: ______________________ __________________________.

10.4: Angles formed by Secants and Tangents Obj: ______________________ __________________________.

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