Warm-Up Exercises ANSWER 58 ANSWER 120 = ( 360 – 120) = 0 1 2 . 2x = 84 + 32 Solve for x.
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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
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