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Solve for x. 1. 2 x = 84 + 32. 1 2. 58. ANSWER. 2. x = ( 360 – 120) = 0. 120. ANSWER. 3. 180 – x = (( 2 x + 4) + 28). 1 2. 82. ANSWER. 45º. ANSWER. Solve for x.

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Solve for x.

1. 2x = 84 + 32

1 2

58

ANSWER

2. x = ( 360 – 120) = 0

120

ANSWER


3.180 – x = (( 2x + 4) + 28).

1 2

82

ANSWER

45º

ANSWER

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.


=

a.

m1

12

(130o)

(125o)

2

=

b.

m KJL

EXAMPLE 1

Find angle and arc measures

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

SOLUTION

= 65o

= 250o


=

m1

12

(210o)

for Example 1

GUIDED PRACTICE

Find the indicated measure.

SOLUTION

= 105o


m RST

(98o)

2

=

for Example 1

GUIDED PRACTICE

Find the indicated measure.

SOLUTION

= 196o


m XY

(80o)

2

=

for Example 1

GUIDED PRACTICE

Find the indicated measure.

SOLUTION

= 160o


The chords JLand KMintersect inside the circle.

(mJM + mLK)

xo

=

12

12

xo

(130o + 156o)

=

xo

= 143

EXAMPLE 2

Find an angle measure inside a circle

Find the value of x.

SOLUTION

Use Theorem 10.12.

Substitute.

Simplify.


The tangent CDand the secant CBintersect outside the circle.

(mAD – mBD)

m BCD

=

12

12

xo

(178o – 76o)

=

x

= 51

EXAMPLE 3

Find an angle measure outside a circle

Find the value of x.

SOLUTION

Use Theorem 10.13.

Substitute.

Simplify.


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


Because between 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.


ANSWER between

y = 61o

for Examples 2, 3, and 4

GUIDED PRACTICE

4. Find the value of the variable.


ANSWER between

a

= 104o

for Examples 2, 3, and 4

GUIDED PRACTICE

Find the value of the variable.

5.


ANSWER between

xo

253.7o

for Examples 2, 3, and 4

GUIDED PRACTICE

6. Find the value of the variable.


Line between t is tangent to the circle. Find the value of x and y.

1.

ANSWER

115

Daily Homework Quiz


ANSWER between

52

Daily Homework Quiz

Line t is tangent to the circle. Find the value of x and y.

2.


ANSWER between

25

Daily Homework Quiz

Line t is tangent to the circle. Find the value of x and y.

3.


ANSWER between

x = 81; y = 40.5

Daily Homework Quiz

Line t is tangent to the circle. Find the value of x and y.

4.


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