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Published byKendall Hart Modified about 1 year ago

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1 Lesson 10-5 Apply Other Angle Relationships in Circles

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2 Angles Inside the Circle Theorem (Interior Angle Theorem) Angles that are formed by two intersecting chords.Definition: The measure of the angle formed by the two intersecting chords is equal to ½ the sum of the measures of the intercepted arcs. Interior Angle Theorem: 1 A B C D E 2

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3 A B C D x°x° 91 85 Example: Interior Angle Theorem y°y°

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4 Practice: 1) 2)

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5 Exterior Angles An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. 3 y x 2 y x 1 x y Two secants A secant and a tangent 2 tangents

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6 Angles Outside the Circle Theorem (Exterior Angle Theorem) The measure of the angle formed is equal to ½ the difference of the intercepted arcs.

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7 Example: Exterior Angle Theorem

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8 Q G F D E C 1 2 3 4 5 6 A 100° 30° 25°

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9 Practice: 1) 2)

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10 An Angle Formed by a Chord and a Tangent 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.

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11 Practice: 1) 2)

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