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

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

8-2 Classifying Angles Problem of the Day 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°

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

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

Course 2 8-2 Classifying Angles A C B 1 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. Angles are measured in degrees (°).

8-2 Classifying Angles An angle’s measure determines the type of Course 2 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°.

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

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

Insert Lesson Title Here Course 2 8-2 Classifying Angles 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

8-2 Classifying Angles If the sum of the measures of two angles is Course 2 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 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 P Q R M Since 60° + 30° = 90°, PMQ and OMP are complementary.

8-2 Classifying Angles Reading Math Course 2 8-2 Classifying Angles 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°. Reading Math

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 mNMO = 15° and mOMR = 165° Since 15° + 165° = 180°, NMO and OMR are supplementary. O N P Q R M Read mNMO as “the measure of angle NMO.” Reading Math

Course 2 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 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 P Q R M Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.

8-2 Classifying Angles Check It Out: Example 2A Course 2 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 mBAC = 35° and mCAF = 145° Since 35° + 145° = 180°, BAC and CAF are supplementary. C B D E F A

8-2 Classifying Angles Check It Out: Example 2B 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 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°. C B D E F A Since 55° + 35° = 90°, CAD and EAF are complementary.

8-2 Classifying Angles Check It Out: Example 2C 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 mBAC = 35° and mEAF = 35° Since 35° + 35° = 70°, BAC and EAF are neither supplementary or complementary. C B D E F A

Additional Example 3: Finding Angle Measures Course 2 8-2 Classifying Angles 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. – 56° – 56° Subtract 56° from both sides to isolate mB. mB = 34° The measure of B = 34°.

8-2 Classifying Angles Check It Out: Example 3 Course 2 8-2 Classifying Angles 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. – 32° – 32° Subtract 32° from both sides to isolate mQ. mQ = 148° The measure of Q = 148°.

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

Insert Lesson Title Here Course 2 8-2 Classifying Angles 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 4. BZC and CZD complementary 5. Angles M and N are supplementary. If M is 117°, what is mN? 63°