Transcript 8-2
8-2 Classifying Angles Warm Up Problem of the Day Lesson Presentation Course 2 8-2 Classifying Angles Warm Up Draw each figure. 1. line segment 2. line 3. ray 4. plane Course 2 8-2 Classifying Angles 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° Course 2 8-2 Classifying Angles Learn to identify angles and angle pairs. Course 2 8-2 Classifying Insert Lesson Title Here Angles Vocabulary angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles Course 2 8-2 Classifying Angles A Vertex An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex. B 1 Angles are measured in degrees (°). Course 2 C 8-2 Classifying 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 8-2 Classifying Angles Additional Example 1: Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. obtuse angle Course 2 B. acute angle 8-2 Classifying Angles Reading Math A• B• 1 • C You can name this angle ABC, CBA, B, or 1. Course 2 8-2 Insert Lesson Title Here Classifying Angles Check It Out: Example 1 Tell whether each angle is acute, right, obtuse, or straight. A. straight angle Course 2 B. acute angle 8-2 Classifying 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 8-2 Classifying Angles Additional Example 2A: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP P Q = 60°. Since 60° + 30° = 90°, PMQ and OMP are complementary. O N M Course 2 R 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 8-2 Classifying Angles Additional Example 2B: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. NMO and OMR mNMO = 15° and mOMR = 165° Since 15° + 165° = 180°, NMO and OMR are supplementary. Reading Math Read mNMO as “the measure of angle NMO.” Course 2 P Q O N M R 8-2 Classifying Angles Additional Example 2C: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. PMQ and QMR To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR P = 75°. Q Since 30° + 75° = 105°, PMQ and QMR are neither complementary O or supplementary. N M Course 2 R 8-2 Classifying Angles Check It Out: Example 2A Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and CAF mBAC = 35° and mCAF = 145° Since 35° + 145° = 180°, BAC and CAF are supplementary. D E C F B A Course 2 8-2 Classifying Angles Check It Out: Example 2B Use the diagram to tell whether the angles are complementary, supplementary, or neither. CAD and EAF To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° - 35° = 55°. mEAF = D 35°. Since 55° + 35° = 90°, C CAD and EAF are complementary. E F B A Course 2 8-2 Classifying Angles Check It Out: Example 2C Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and EAF mBAC = 35° and mEAF = 35° Since 35° + 35° = 70°, BAC and EAF are neither supplementary C or complementary. D E F B A Course 2 8-2 Classifying Angles Additional Example 3: Finding Angle Measures Angles A and B are complementary. If mA is 56°, what is the mB? Since A and B are complementary, mA + mB = 90°. mA + mB = 90° 56° + mB = 90° – 56° – 56° mB = 34° Substitute 56° for mA. Subtract 56° from both sides to isolate mB. The measure of B = 34°. Course 2 8-2 Classifying Angles Check It Out: Example 3 Angles P and Q are supplementary. If mP is 32°, what is the mQ? Since P and Q are complementary, mP + mQ = 180°. mP + mQ = 180° 32° + mQ = 180° – 32° – 32° mQ = 148° Substitute 32° for mP. Subtract 32° from both sides to isolate mQ. The measure of Q = 148°. Course 2 8-2 Classifying Insert Lesson Angles Title Here Lesson Quiz: Part I Tell whether each angle is acute, right, obtuse, or straight. 1. straight 2. obtuse Course 2 8-2 Classifying Insert Lesson Angles Title Here Lesson Quiz: Part II Use the diagram to tell whether the angles are complementary, supplementary, or neither. 3. AZB and BZC neither 4. BZC and CZD complementary 5. Angles M and N are supplementary. If M is 117°, what is mN? 63° Course 2