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8-2

8-2. Classifying Angles. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 8-2. Classifying Angles. Course 2. Warm Up Draw each figure. 1. line segment 2. line 3. ray 4. plane. 8-2. Classifying Angles. Course 2. Problem of the Day

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8-2

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  1. 8-2 Classifying Angles Course 2 Warm Up Problem of the Day Lesson Presentation

  2. 8-2 Classifying Angles Course 2 Warm Up Draw each figure. 1.line segment 2. line 3. ray 4. plane

  3. 8-2 Classifying Angles Course 2 Problem of the Day Find the measure of the smaller angle between the hour and minute hands on a clock at eight o’clock? 120°

  4. 8-2 Classifying Angles Course 2 Learn to identify angles and angle pairs.

  5. 8-2 Classifying Angles Course 2 Insert Lesson Title Here Vocabulary angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles

  6. 8-2 Classifying Angles A Vertex 1 B C Course 2 An angleis formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex. Angles are measured in degrees (°).

  7. 8-2 Classifying Angles Course 2 An angle’s measure determines the type of angle it is. A right angle is an angle that that measures exactly 90°. The symbol indicates a right angle. An acute angle is an angle that measures less than 90°. Anobtuse angle is an angle that measures more than 90° but less than180°. A straightangle is an angle that measures 180°.

  8. 8-2 Classifying Angles Course 2 Additional Example 1: Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. B. acute angle obtuse angle

  9. 8-2 Classifying Angles A • 1 B• •C Reading Math You can name this angle ABC, CBA, B, or 1. Course 2

  10. 8-2 Classifying Angles Course 2 Insert Lesson Title Here Check It Out: Example 1 Tell whether each angle is acute, right, obtuse, or straight. B. A. straight angle acute angle

  11. 8-2 Classifying Angles Course 2 If the sum of the measures of two angles is 90°, then the angles are complementary angles. If the sum of the measures of two angles is 180°, then the angles are supplementary angles.

  12. 8-2 Classifying Angles P Q To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mOMP = 60°. O N R M Course 2 Additional Example 2A: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ Since 60° + 30° = 90°, PMQ andOMP are complementary.

  13. 8-2 Classifying Angles Reading Math If the angle you are measuring appears obtuse, then it measure is greater than 90°. If the angle is acute, its measure is less than 90°. Course 2

  14. 8-2 Classifying Angles P Q O N R M Reading Math Read mNMO as “the measure of angle NMO.” Course 2 Additional Example 2B: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. NMO and OMR mNMO = 15° and mOMR = 165° Since 15° + 165° = 180°, NMO andOMR are supplementary.

  15. 8-2 Classifying Angles P Q To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mQMR = 75°. O N R M Course 2 Additional Example 2C: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. PMQ and QMR Since 30° + 75° = 105°, PMQ andQMR are neither complementary or supplementary.

  16. 8-2 Classifying Angles D E C F B A Course 2 Check It Out: Example 2A Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and CAF mBAC = 35° and mCAF = 145° Since 35° + 145° = 180°, BAC andCAF are supplementary.

  17. 8-2 Classifying Angles To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° -35° = 55°. mEAF = 35°. D E C F B A Course 2 Check It Out: Example 2B Use the diagram to tell whether the angles are complementary, supplementary, or neither. CAD and EAF Since 55° + 35° = 90°, CAD andEAF are complementary.

  18. 8-2 Classifying Angles D E C F B A Course 2 Check It Out: Example 2C Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and EAF mBAC = 35° and mEAF = 35° Since 35° + 35° = 70°, BAC andEAF are neither supplementary or complementary.

  19. 8-2 Classifying Angles Course 2 Additional Example 3: Finding Angle Measures Angles A and B are complementary. If mA is 56°, what is the mB? Since A and B are complementary, mA + mB = 90°. mA + mB = 90° 56° + mB = 90° Substitute 56° for mA. Subtract 56° from both sides to isolate mB. – 56° – 56° mB = 34° The measure of B = 34°.

  20. 8-2 Classifying Angles Course 2 Check It Out: Example 3 Angles P and Q are supplementary. If mP is 32°, what is the mQ? Since P and Q are complementary, mP + mQ = 180°. mP + mQ = 180° 32° + mQ = 180° Substitute 32° for mP. Subtract 32° from both sides to isolate mQ. – 32°– 32° mQ = 148° The measure of Q = 148°.

  21. 8-2 Classifying Angles 2. Course 2 Insert Lesson Title Here Lesson Quiz: Part I Tell whether each angle is acute, right, obtuse, or straight. straight 1. obtuse

  22. 8-2 Classifying Angles Course 2 Insert Lesson Title Here Lesson Quiz: Part II Use the diagram to tell whether the angles are complementary, supplementary, or neither. 3. AZB and BZC neither complementary 4. BZC and CZD 5. Angles M and N are supplementary. If M is 117°, what is mN? 63°

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