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Explore Angles: Classification and Measurement

Learn to identify and classify angles with this interactive course. Understand angle pairs, measurements, and types (right, acute, obtuse, straight). Practice finding complementary and supplementary angles as you enhance your geometry skills.

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Explore Angles: Classification and Measurement

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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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