Warm-Up Exercises

ANSWER 58

ANSWER 120

2. x = ( 360 – 120) = 01 2

1. 2x = 84 + 32

Solve for x.

Warm-Up Exercises

ANSWER 82

3. 180 – x = (( 2x + 4) + 28).1 2

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.

Solve for x.

ANSWER 45º

Warm-Up ExercisesEXAMPLE 1 Find angle and arc measures

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

SOLUTION

= 12 (130o) = 65o

= 2 (125o) = 250ob. m KJL

a. m 1

Warm-Up ExercisesGUIDED PRACTICE for Example 1

Find the indicated measure.

SOLUTION

= 12 (210o) = 105om 1

Warm-Up ExercisesGUIDED PRACTICE for Example 1

Find the indicated measure.

= 2 (98o) = 196om RST

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Example 1

Find the indicated measure.

= 2 (80o) = 160om XY

SOLUTION

Warm-Up ExercisesEXAMPLE 2 Find an angle measure inside a circle

Find the value of x.

SOLUTION

The chords JL and KM intersect inside the circle.

Use Theorem 10.12.xo = 12

(mJM + mLK)

xo = 12

(130o + 156o) Substitute.

xo = 143 Simplify.

Warm-Up ExercisesEXAMPLE 3 Find an angle measure outside a circle

Find the value of x.

SOLUTION

Use Theorem 10.13.

Substitute.

Simplify.

The tangent CD and the secant CB intersect outside the circle.

= 12

(178o – 76o)xo

= 51 x

m BCD (mAD – mBD)= 12

Warm-Up ExercisesEXAMPLE 4 Solve a real-world problem

SCIENCE

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.)

Warm-Up ExercisesEXAMPLE 4 Solve a real-world problem

SOLUTION

Use Theorem 10.13.

Substitute.149o 12

[(360o – xo) –xo]

Solve for x.xo 31

= 12

m BCD (mDEB – mBD)

Because CB and CD are tangents,CB AB and CD AD

Also,BC DC and CA CA . So, ABC ADC by the Hypotenuse-Leg Congruence Theorem, and BCA DCA.Solve right CBA to find that m BCA 74.5°.

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

Warm-Up ExercisesGUIDED PRACTICE for Examples 2, 3, and 4

4. Find the value of the variable.

y = 61o

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 2, 3, and 4

Find the value of the variable.5.

= 104o a

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 2, 3, and 4

6. Find the value of the variable.

xo 253.7o

ANSWER

Warm-Up ExercisesDaily Homework Quiz

ANSWER 115

1.

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

Warm-Up ExercisesDaily Homework Quiz

2.

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

ANSWER 52

Warm-Up ExercisesDaily Homework Quiz

3.

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

ANSWER 25

Warm-Up ExercisesDaily Homework Quiz

4.

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

ANSWER x = 81; y = 40.5