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Warm-up

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. 10.4 Other Angle Relationships in Circles. Theorem 10.12.

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Warm-up

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  1. 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

  2. 10.4 Other Angle Relationships in Circles

  3. Theorem 10.12 • 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. • m∠1 = ½ mAB • m∠2 = ½ mBDA D 2 1

  4. Find mGF m∠FGD = ½ mGF 180∘ - 122∘ = ½ mGF 58∘ = ½ mGF 116∘ = mGF D

  5. Find m∠EFH m∠EFH = ½ mFH m∠EFH = ½ (130) = 65∘ D

  6. Find mSR m∠SRQ = ½ mSR 71∘ = ½ mSR 142∘ = ½ mSR 142∘ = mSR

  7. 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)

  8. Find m∠AEB m∠AEB = ½ (mAB + mCD = ½ (139∘+ 113∘) = ½ (252∘) = 126∘

  9. Find m∠RNM m∠MNQ = ½ (mMQ + mRP = ½ (91∘+ 225∘) = 158∘ m∠RNM = 180∘ -∠MNQ = 180∘ -158∘ = 22∘

  10. Find m∠ABD m∠ABD = ½ (mEC + mAD) = ½ (37∘+ 65∘) = ½ (102∘) = 51∘

  11. 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.

  12. Find the value of x. 63∘ 40∘

  13. Find the value of x. 33∘

  14. In the company logo shown, mFH = 108∘, and mLJ = 12∘. What is m∠FKH 48∘

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