Warm-up Solve the equations 4c = 180 ½ (3x+42) = 27 8y = ½ (5y+55) 120 = ½ [(360-x) – x] c= 45...
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Transcript of Warm-up Solve the equations 4c = 180 ½ (3x+42) = 27 8y = ½ (5y+55) 120 = ½ [(360-x) – x] c= 45...
![Page 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/1.jpg)
Warm-upSolve the equations4c = 180
½ (3x+42) = 27
8y = ½ (5y+55)
120 = ½ [(360-x) – x]
c= 45x=4y=5x=60
![Page 2: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/2.jpg)
10.4 Other Angle Relationships in Circles
![Page 3: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/3.jpg)
Theorem 10.12If 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
![Page 4: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/4.jpg)
Find mGF
m∠FGD = ½ mGF 180∘ - 122∘ = ½ mGF
58∘
= ½ mGF
116∘
= mGF
D
![Page 5: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/5.jpg)
Find m∠EFH
m∠EFH = ½ mFH m∠EFH = ½ (130)
= 65∘
D
![Page 6: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/6.jpg)
Find mSR
m∠SRQ = ½ mSR 71∘ = ½ mSR
142∘
= ½ mSR
142∘
= mSR
![Page 7: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/7.jpg)
Theorem 10.13If 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)
![Page 8: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/8.jpg)
Find m∠AEB
m∠AEB = ½ (mAB + mCD
= ½ (139∘ + 113∘)= ½ (252∘)= 126∘
![Page 9: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/9.jpg)
Find m∠RNM
m∠MNQ = ½ (mMQ + mRP= ½ (91∘ + 225∘)= 158∘
m∠RNM = 180∘ - ∠MNQ= 180∘ - 158∘
= 22∘
![Page 10: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/10.jpg)
Find m∠ABD
m∠ABD = ½ (mEC + mAD)
= ½ (37∘ + 65∘)= ½ (102∘)= 51∘
![Page 11: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/11.jpg)
Theorem 10.14If 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.
![Page 12: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/12.jpg)
Find the value of x.
40∘ 63∘
![Page 13: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/13.jpg)
Find the value of x.
33∘
![Page 14: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697c0211a28abf838cd2aea/html5/thumbnails/14.jpg)
In the company logo shown, mFH = 108∘, and mLJ = 12∘. What is m∠FKH
48∘