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Angles Formed by Tangents, Chords, and Secants

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Tangent: A line that intersects the circle in exactly one point. PT is a tangent P T A

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Angle Formed by Tangent and Chord: The measure of an angle formed by a tangent and a chord intersecting at the point of tangency is one-half the measure of the intercepted arc. P T A

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Angles Formed by Two Chords In a Circle: The measure of an angle formed by two chords intersecting in a circle is one-half the sum of the measures of the arcs intercepted by the angle and by its vertical angle. A B C D E

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1. If mAC = 30 and m AEC = 55, find mBD. A B C D E

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2. If mAC = 20 and mBD = 100, find m AEC. A B C D E

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3. If mCB = 120 and mAD = 180, find m AED. A B C D E

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4. If mAC = 27 and mDB = 81, find m DEB. A B C D E

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5. If mAC = 20 and m AEC = 70, find mBD. A B C D E

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6. If mBD = 75 and m DEB = 60, find mAC. A B C D E

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7. If mAB = 100 find m ABC. A B C D

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8. m ABC = 75, find mAB. A B C D

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9. If m ABD = 110, find mAEB. A B C D E

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10. If mAEB = 105, find m ABD A B C D E

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