# Angles Formed by Tangents, Chords, and Secants

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Angles Formed by Tangents, Chords, and Secants

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

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

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

1. If mAC = 30 and mAEC = 55, find mBD.

2. If mAC = 20 and mBD = 100, find mAEC.

3. If mCB = 120 and mAD = 180, find mAED.

4. If mAC = 27 and mDB = 81, find mDEB.

5. If mAC = 20 and mAEC = 70, find mBD.

6. If mBD = 75 and mDEB = 60, find mAC.

7. If mAB = 100 find mABC. A B C D

8. mABC = 75, find mAB. A B C D

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

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