12 5 Angle Relationshipsinin Circles Warm Up Lesson

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12 -5 Angle. Relationshipsinin. Circles Warm Up Lesson Presentation Lesson Quiz Holt. Mc. Dougal

12 -5 Angle. Relationshipsinin. Circles Warm Up Lesson Presentation Lesson Quiz Holt. Mc. Dougal Geometry Holt

12 -5 Angle Relationships in Circles Objectives Find the measures of angles formed by

12 -5 Angle Relationships in Circles Objectives Find the measures of angles formed by lines that intersect circles. Use angle measures to solve problems. Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Example 1 A: Using Tangent-Secant and Tangent-Chord Angles

12 -5 Angle Relationships in Circles Example 1 A: Using Tangent-Secant and Tangent-Chord Angles Find each measure. m EFH = 65° Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Example 1 B: Using Tangent-Secant and Tangent-Chord Angles

12 -5 Angle Relationships in Circles Example 1 B: Using Tangent-Secant and Tangent-Chord Angles Find each measure. Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Check It Out! Example 1 a Find each

12 -5 Angle Relationships in Circles Check It Out! Example 1 a Find each measure. m STU = 83 Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Check It Out! Example 1 b Find each

12 -5 Angle Relationships in Circles Check It Out! Example 1 b Find each measure. Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Example 2: Finding Angle Measures Inside a Circle

12 -5 Angle Relationships in Circles Example 2: Finding Angle Measures Inside a Circle Find each measure. m AEB = 126 Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Check It Out! Example 2 a Find each

12 -5 Angle Relationships in Circles Check It Out! Example 2 a Find each angle measure. m ABD Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Check It Out! Example 2 b Find each

12 -5 Angle Relationships in Circles Check It Out! Example 2 b Find each angle measure. m RNM = 180° – MNQ m RNM = 180° – 158° = 22° Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Example 3: Finding Measures Using Tangents and Secants

12 -5 Angle Relationships in Circles Example 3: Finding Measures Using Tangents and Secants Find the value of x. = 40 Holt Mc. Dougal Geometry = 63

12 -5 Angle Relationships in Circles Check It Out! Example 3 Find the value

12 -5 Angle Relationships in Circles Check It Out! Example 3 Find the value of x. 50° = 83° – x x = 33° Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Example 4: Design Application In the company logo

12 -5 Angle Relationships in Circles Example 4: Design Application In the company logo shown, and = 12°. What is m FKH? Holt Mc. Dougal Geometry = 108°,

12 -5 Angle Relationships in Circles Check It Out! Example 4 Two of the

12 -5 Angle Relationships in Circles Check It Out! Example 4 Two of the six muscles that control eye movement are attached to the eyeball and intersect behind the eye. If m. AEB = 225 , what is m ACB? Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Example 5: Finding Arc Measures Find Step 1

12 -5 Angle Relationships in Circles Example 5: Finding Arc Measures Find Step 1 Find U V If a tangent and a secant intersect on a at the pt. of tangency, then the measure of the formed is half the measure of its intercepted arc. Substitute 180 – 113 for m XVY and 68 for m. WZ Multiply both sides by 2. Subtract 68 from both sides. Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Example 5 Continued U Step 2 Find V

12 -5 Angle Relationships in Circles Example 5 Continued U Step 2 Find V Thm. 11 -5 -3 Substitute the given values. Multiply both sides by 2. Add 66 to both sides. Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Check It Out! Example 5 Find m. LP

12 -5 Angle Relationships in Circles Check It Out! Example 5 Find m. LP Step 1 Find Step 2 Find Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Lesson Quiz: Part I Find each measure. 1.

12 -5 Angle Relationships in Circles Lesson Quiz: Part I Find each measure. 1. m FGJ 41. 5° 2. m HJK 65° Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Lesson Quiz: Part II 3. An observer watches

12 -5 Angle Relationships in Circles Lesson Quiz: Part II 3. An observer watches people riding a Ferris wheel that has 12 equally spaced cars. Find x. 30° Holt Mc. Dougal Geometry

12 -5 Angle Relationships in Circles Lesson Quiz: Part III 4. Find m. CE.

12 -5 Angle Relationships in Circles Lesson Quiz: Part III 4. Find m. CE. 12° Holt Mc. Dougal Geometry