WarmUp Exercises Solve for x 1 2 x

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Warm-Up Exercises Solve for x. 1. 2 x = 84 + 32 ANSWER 2.

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

Warm-Up Exercises Solve for x. 3. 1 180 – x = (( 2 x

Warm-Up Exercises Solve for x. 3. 1 180 – x = (( 2 x + 4) + 28). 2 ANSWER 82 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. ANSWER 45º

Warm-Up 1 Exercises EXAMPLE Find angle and arc measures Line m is tangent to

Warm-Up 1 Exercises EXAMPLE Find angle and arc measures Line m is tangent to the circle. Find the measure of the red angle or arc. SOLUTION a. m 1 1 = 2 (130 o) = 65 o o (125 ) = 250 o 2 b. m KJL =

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION 1 m

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION 1 m 1 = 2 (210 o) = 105 o

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION o (98

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION o (98 ) 2 = m RST = 196 o

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION o (80

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION o (80 ) 2 = m XY = 160 o

Warm-Up 2 Exercises EXAMPLE Find an angle measure inside a circle Find the value

Warm-Up 2 Exercises EXAMPLE Find an angle measure inside a circle Find the value of x. SOLUTION The chords JL and KM intersect inside the circle. 1 (m. JM + m. LK) Use Theorem 10. 12. xo = 2 xo = 1 (130 o + 156 o) 2 xo = 143 Substitute. Simplify.

Warm-Up 3 Exercises EXAMPLE Find an angle measure outside a circle Find the value

Warm-Up 3 Exercises EXAMPLE Find an angle measure outside a circle Find the value of x. SOLUTION The tangent CD and the secant CB intersect outside the circle. 1 (m. AD – m. BD) Use Theorem 10. 13. m BCD = 2 xo = 1 (178 o – 76 o) 2 x = 51 Substitute. Simplify.

Warm-Up 4 Exercises EXAMPLE Solve a real-world problem SCIENCE The Northern Lights are bright

Warm-Up 4 Exercises EXAMPLE 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 4 Exercises EXAMPLE Solve a real-world problem SOLUTION Because CB and CD are

Warm-Up 4 Exercises EXAMPLE Solve a real-world problem SOLUTION 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°. 1 (m. DEB – m. BD) Use Theorem 10. 13. m BCD = 2 1 149 o [(360 o – xo) –xo] Substitute. 2 xo Solve for x. 31 ANSWER The measure of the arc from which the flash is visible is about 31 o.

Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 4. Find the value

Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 4. Find the value of the variable. ANSWER y = 61 o

Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 5. Find the value

Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 5. Find the value of the variable. ANSWER a = 104 o

Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 6. Find the value

Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 6. Find the value of the variable. ANSWER xo 253. 7 o

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the value of x and y. 1. ANSWER 115

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the value of x and y. 2. ANSWER 52

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the value of x and y. 3. ANSWER 25

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the

Daily Homework Quiz Warm-Up Exercises Line t is tangent to the circle. Find the value of x and y. 4. ANSWER x = 81; y = 40. 5

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