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Learn to identify angles and angle pairs.

This educational resource provides an in-depth exploration of angles and angle pairs, including definitions and classifications. Learn to identify key types of angles, such as acute, right, obtuse, and straight angles, and understand the concepts of complementary and supplementary angles. Discover how to measure angles in degrees and apply this knowledge to various examples and quizzes designed to reinforce learning. Master the fundamentals of angle measurement and classification for better comprehension in geometry.

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Learn to identify angles and angle pairs.

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  1. Learn to identify angles and angle pairs.

  2. Vocabulary angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles

  3. A Vertex 1 B C 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 (°).

  4. 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 than 180°. A straightangle is an angle that measures exactly 180°.

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

  6. Reading Math You can name this angle ABC, CBA, B, or 1. A • 1 B• •C

  7. 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.

  8. 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°. P Q O N R M 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.

  9. Reading Math If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle is acute, its measure is less than 90°.

  10. P Q Reading Math O Read mNMO as “the measure of angle NMO.” N R M 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.

  11. 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°. P Q O N R M 8-2 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 nor supplementary.

  12. 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. – 56° – 56° mB = 34° The measure of B = 34°.

  13. Lesson Quiz for Student Response Systems • 1. Identify the type of the given angle. A. acute B. obtuse C. right D. straight

  14. Lesson Quiz for Student Response Systems • 2. Identify the type of the given angle. A. acute B. obtuse C. right D. straight

  15. Lesson Quiz for Student Response Systems • 3. Use the diagram to identify the type of the given pair of angles. mAOB and mBOD A. complementary B. supplementary C. right D. none

  16. Lesson Quiz for Student Response Systems • 4. Angles A and B are complementary. If mA is 36°, what is mB? A.54° B.90° C.126° D.144°

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