1 / 14

# Warm-up - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Warm-up' - lark

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

• 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

• 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

m∠FGD = ½ mGF

180∘ - 122∘ = ½ mGF

58∘ = ½ mGF

116∘ = mGF

D

Find m∠EFH

m∠EFH = ½ mFH

m∠EFH = ½ (130)

= 65∘

D

Find mSR

m∠SRQ = ½ mSR

71∘ = ½ mSR

142∘ = ½ mSR

142∘ = mSR

• 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

m∠AEB = ½ (mAB + mCD

= ½ (139∘+ 113∘)

= ½ (252∘)

= 126∘

Find m∠RNM

m∠MNQ = ½ (mMQ + mRP

= ½ (91∘+ 225∘)

= 158∘

m∠RNM = 180∘ -∠MNQ

= 180∘ -158∘

= 22∘

Find m∠ABD

m∠ABD = ½ (mEC + mAD)

= ½ (37∘+ 65∘)

= ½ (102∘)

= 51∘

• 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.

63∘

40∘

33∘

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

48∘