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7-2 Angles Warm Up Problem of the Day Lesson Presentation Course 2 7-2 Angles Warm Up Draw each figure. 1. line segment 2. line 3. ray 4. plane Course 2 7-2 Angles Problem of the Day What is the measure of the smaller angle between the hour hand and the minute hand on a clock at eight o’clock? 120° Course 2 7-2 Angles Learn to identify angles and parts of angles. Course 2 7-2 Angles Insert Lesson Title Here Vocabulary angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles Course 2 7-2 Angles An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is is the vertex. A Vertex 1 B C You can name an angle in three ways: • with the capital letter at the vertex: • with the number inside the angle: B, 1, • with three capital letters so that the letter CBA at the vertex is in the middle: ABC or Course 2 7-2 Angles Angles are measured in degrees (°). You can use a protractor to measure an angle. The measure of Course 2 XYZ is 122°, or m XYZ = 122°. 7-2 Angles Additional Example 1A & 1B: Identifying Angle Measures Give the measurement of each angle. A. STV m STV = 55° B. Course 2 XTU m XTU = 25° 7-2 Angles Additional Example 1C &1D: Identifying Angle Measures Give the measurement of each angle. C. WTU m WTU = 40° + 25° m WTU = 65° D. STX m STX = 55° + 60° + 40° m Course 2 STX = 155° 7-2 Insert AnglesLesson Title Here Try This: Example 1 Give the measure of each angle. A. STV m STV = 35° B. Course 2 XTU m XTU = 40° W V S 55° 50° 35° 40° T X U 7-2 Insert AnglesLesson Title Here Try This: Example 1 Continued Give the measure of each angle. C. WTU m WTU = 50° + 40° m WTU = 90° W V S D. STX m STX = 35° + 55° + 50° m Course 2 STX = 140° 55° 50° 35° 40° T X U 7-2 Angles 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° An obtuse angle is an angle that measures more than 90° but less than180° A straight angle is an angle that measures 180° Course 2 7-2 Angles Additional Example 2: Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. B. right angle Course 2 obtuse angle C. acute angle 7-2 Insert AnglesLesson Title Here Try This: Example 2 Tell whether each angle is acute, right, obtuse, or straight. B. C. A. straight angle Course 2 acute angle obtuse angle 7-2 Angles 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. Course 2 7-2 Angles Additional Example 3A: Identifying Complementary and Supplementary Angles Use the figure to name the following. A. one pair of complementary angles m OMP = 30° and m OMR = 60° Since 30° + 60° = 90°, OMP and OMR are complementary. N Q 60° 90° M R Course 2 P 30° O 60° 7-2 Angles Additional Example 3B: Identifying Complementary and Supplementary Angles Use the figure to name the following. B. one pair of supplementary angles m RMO = 60° and N Q 60° 90° m QMO = 90° + 30° = 120° Since 60° + 120° = 180°, RMO and QMO are supplementary. Course 2 M R P 30° O 60° 7-2 Angles Try This: Example 3A Use the figure to name the following. A. one pair of complementary angles m OMP = 30° and m NMQ = 60° Since 30° + 60° = 90°, OMP and NMQ are complementary. N Q 60° 90° M R Course 2 P 30° O 60° 7-2 Angles Try This: Example 3B Use the figure to name the following. B. one pair of supplementary angles m QMP = 90° and N Q 60° 90° m PMR = 30° + 60° = 90° Since 90° + 90° = 180°, QMP and PMR are supplementary. Course 2 M R P 30° O 60° 7-2 Angles Insert Lesson Title Here Lesson Quiz Give the measure of each angle, and tell whether it is acute, obtuse, right, or straight. 1. 2. 3. AFB 90°; right AFC 140°; obtuse DFC 40°; acute A E F D 40° 4. Name a pair of complementary angles. DFC and CFB 5. Name a pair of supplementary angles. Possible answer: EFA and AFB Course 2 B 50° C