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### 10.4 Other Angle Relationships in Circles

Warm-up

- Solve the equations
4c = 180

½ (3x+42) = 27

8y = ½ (5y+55)

120 = ½ [(360-x) – x]

c= 45

x=4

y=5

x=60

Theorem 10.12

- If a tangent and a chord intersect at point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
- m∠1 = ½ mAB
- m∠2 = ½ mBDA

D

2

1

Theorem 10.13

- If two chords intersect in the interior of a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

2

m∠1 = ½ (mCD + mAB),

m∠2 = ½(mBD + mAC)

Theorem 10.14

- If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

Find the value of x.

33∘

In the company logo shown, mFH = 108∘, and mLJ = 12∘. What is m∠FKH

48∘

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