Warm-Up Exercises ANSWER 58 ANSWER 120 2.x = ( 360 – 120) = 0 1212 1.2x = 84 + 32 Solve for x.

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Presentation transcript:

Warm-Up Exercises ANSWER 58 ANSWER x = ( 360 – 120) = x = Solve for x.

Warm-Up Exercises ANSWER – x = (( 2x + 4) + 28) 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 Exercises EXAMPLE 1 Find angle and arc measures Line m is tangent to the circle. Find the measure of the red angle or arc. SOLUTION = 1212 (130 o ) = 65 o = 2 (125 o ) = 250 o b.m KJL a.m 1

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION = 1212 (210 o ) = 105 o m 1

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

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

Warm-Up Exercises EXAMPLE 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 xoxo = 1212 (mJM + mLK) xoxo = 1212 (130 o o ) Substitute. xoxo = 143 Simplify.

Warm-Up Exercises EXAMPLE 3 Find an angle measure outside a circle Find the value of x. SOLUTION Use Theorem Substitute. Simplify. The tangent CD and the secant CB intersect outside the circle. = 1212 (178 o – 76 o ) xoxo = 51 x m BCD (mAD – mBD) = 1212

Warm-Up Exercises EXAMPLE 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 Exercises EXAMPLE 4 Solve a real-world problem SOLUTION Use Theorem Substitute. 149 o 1212 [(360 o – x o ) –x o ] Solve for x. xoxo 31 = 1212 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°. 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 of the variable. y = 61 o ANSWER

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

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

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

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

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

Warm-Up Exercises Daily Homework Quiz 4. Line t is tangent to the circle. Find the value of x and y. ANSWER x = 81; y = 40.5