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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

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

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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