Apply other angle relationships in circles
This presentation is the property of its rightful owner.
Sponsored Links
1 / 26

Apply Other Angle Relationships in Circles PowerPoint PPT Presentation


  • 125 Views
  • Uploaded on
  • Presentation posted in: General

Apply Other Angle Relationships in Circles. Sunday, September 14, 2014. Essential Question: How do we find the measures of angles inside or outside a circle?. Lesson 6.5. M2 Unit 3: Day 5. Find the value of x. 1. ANSWER. ANSWER. 38. 56. Daily Homework Quiz. Daily Homework Quiz. 2.

Download Presentation

Apply Other Angle Relationships in Circles

An Image/Link below is provided (as is) to download presentation

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


Apply other angle relationships in circles

Apply Other Angle Relationships in Circles

Sunday, September 14, 2014

Essential Question:

How do we find the measures of angles inside or outside a circle?

Lesson 6.5

M2 Unit 3: Day 5


Apply other angle relationships in circles

Find the value of x .

1.

ANSWER

ANSWER

38

56

Daily Homework Quiz

Daily Homework Quiz

2.


Apply other angle relationships in circles

ANSWER

ANSWER

44

x = 54; y = 20

Daily Homework Quiz

Find the value of x .

3.

4.


Apply other angle relationships in circles

ANSWER

x = 5; y = 10

Daily Homework Quiz

Find the value of each variable.

5.


Apply other angle relationships in circles

Solve for x.

1.2x = 84 + 32

1 2

58

ANSWER

2.x = ( 360 – 120) = 0

120

ANSWER

Warm Ups


Apply other angle relationships in circles

3.180 – x = (( 2x + 4) + 28).

1 2

82

ANSWER

45º

ANSWER

Warm Ups

Solve for x.

4.One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle.


Theorem 6 13

Theorem 6.13

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.


Apply other angle relationships in circles

=

a.

m1

12

(130o)

(125o)

2

=

b.

m KJL

Find angle and arc measures

EXAMPLE

Line mis tangent to the circle. Find the measure of the red angle or arc.

SOLUTION

= 65o

= 250o


Apply other angle relationships in circles

=

m1

12

(210o)

GUIDED PRACTICE

Guided Practice

Find the indicated measure.

SOLUTION

= 105o


Apply other angle relationships in circles

m TSR

(98o)

2

=

GUIDED PRACTICE

Guided Practice

Find the indicated measure.

SOLUTION

= 196o


Apply other angle relationships in circles

m XY

(80o)

2

=

GUIDED PRACTICE

Guided Practice

Find the indicated measure.

SOLUTION

= 160o


Theorem 6 14 angle inside the circle

Theorem 6.14 Angle Inside the Circle

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 arc intercepted by the angle and its vertical angle.


Apply other angle relationships in circles

The chords JLand KMintersect inside the circle.

(mJM + mLK)

xo

=

12

12

xo

(130o + 156o)

=

xo

= 143

EXAMPLE 2

EXAMPLE

Find the value of x.

SOLUTION

Use Theorem 6.14.

Substitute.

Simplify.


Apply other angle relationships in circles

The chords ACand CDintersect inside the circle.

=

12

12

78o

(yo + 95o)

=

61

= y

Guided Practice

4. Find the value of the variable.

SOLUTION

(mAB + mCD)

78°

Use Theorem 6.14

Substitute.

Simplify.


Theorem 6 15 angle outside the circle

Theorem 6.15Angle Outside the Circle


Theorem 6 15 secant and tangent

Theorem 6.15 Secant and Tangent


Theorem 6 15 two tangents

Theorem 6.15Two Tangents


Theorem 6 15 two secants

Theorem 6.15 Two Secants


Apply other angle relationships in circles

The tangent CDand the secant CBintersect outside the circle.

(mAD – mBD)

m BCD

=

12

12

xo

(178o – 76o)

=

x

= 51

EXAMPLE

Find an angle measure outside a circle

Find the value of x.

SOLUTION

Use Theorem 10.13.

Substitute.

Simplify.


Apply other angle relationships in circles

EXAMPLE

Find an angle measure outside a circle

Find the value of x.

= 40

= 63


Apply other angle relationships in circles

SOLUTION

The tangent JFand the secant JGintersect outside the circle.

(mFG – mKH)

m FJG

=

12

12

30o

(ao – 44o)

=

a

= 104

GUIDED PRACTICE

Guided Practice

Find the value of the variable.

5.

Use Theorem 10.13.

Substitute.

Simplify.


Apply other angle relationships in circles

Because QTand QRare tangents,

Also,TS SR and CA CA . So, QTS QRS by the Hypotenuse-Leg Congruence Theorem, and

(mTUR – mTR)

m TQR

QR RS and QT TS

12

12

TQS RQS.Solve rightQTS to find thatm RQS

73.7°.

=

73.7o

[(xo) –(360 –x)o]

xo

253.7

GUIDED PRACTICE

Guided Practice

6. Find the value of the variable.

SOLUTION

Use Theorem 10.13.

Substitute.

Solve for x.


Apply other angle relationships in circles

Guided Practice

7. Find the value of x.

50° = 83° – x

x = 33°


Apply other angle relationships in circles

The Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth. Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth from which the flash is visible? (Earth’s radius is approximately 4000 miles.)

EXAMPLE 4

Solve a real-world problem

SCIENCE


Apply other angle relationships in circles

Because CBand CDare tangents,

Also,BC DC and CA CA . So, ABC ADC by the Hypotenuse-Leg Congruence Theorem, and

BCA DCA.Solve rightCBA to find thatm BCA

74.5°.

(mDEB – mBD)

m BCD

=

CB AB and CD AD

12

12

149o

[(360o – xo) –xo]

xo

31

The measure of the arc from which the flash is visible is about 31o.

ANSWER

EXAMPLE 4

Solve a real-world problem

SOLUTION

Use Theorem 10.13.

Substitute.

Solve for x.


Homework

Homework

Page 214 # 1 – 15 all


  • Login