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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
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

10.4 Other Angle Relationships in Circles


Theorem 10 12
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


Find mgf
Find mGF

m∠FGD = ½ mGF

180∘ - 122∘ = ½ mGF

58∘ = ½ mGF

116∘ = mGF

D


Find m efh
Find m∠EFH

m∠EFH = ½ mFH

m∠EFH = ½ (130)

= 65∘

D


Find msr
Find mSR

m∠SRQ = ½ mSR

71∘ = ½ mSR

142∘ = ½ mSR

142∘ = mSR


Theorem 10 13
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)


Find m aeb
Find m∠AEB

m∠AEB = ½ (mAB + mCD

= ½ (139∘+ 113∘)

= ½ (252∘)

= 126∘


Find m rnm
Find m∠RNM

m∠MNQ = ½ (mMQ + mRP

= ½ (91∘+ 225∘)

= 158∘

m∠RNM = 180∘ -∠MNQ

= 180∘ -158∘

= 22∘


Find m abd
Find m∠ABD

m∠ABD = ½ (mEC + mAD)

= ½ (37∘+ 65∘)

= ½ (102∘)

= 51∘


Theorem 10 14
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
Find the value of x.

63∘

40∘



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

48∘


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