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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 mAEC = 55, find mBD.**

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**2. If mAC = 20 and mBD = 100, find mAEC.**

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**3. If mCB = 120 and mAD = 180, find mAED.**

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**4. If mAC = 27 and mDB = 81, find mDEB.**

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**5. If mAC = 20 and mAEC = 70, find mBD.**

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**6. If mBD = 75 and mDEB = 60, find mAC.**

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7. If mAB = 100 find mABC. A B C D

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8. mABC = 75, find mAB. A B C D

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

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

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Geometry Section 10.4 Angles Formed by Secants and Tangents

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