Classifying Angles Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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

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°

Classifying Angles Learn to identify angles and angle pairs.

Classifying Angles Vocabulary angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles

Classifying 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 the vertex. Angles are measured in degrees (°). A C B 1 Vertex

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 than 180°. A straight angle is an angle that measures exactly 180°.

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

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

Classifying Angles Check It Out: Example 1 Tell whether each angle is acute, right, obtuse, or straight. A. B. straight angle acute angle

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.

Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2A: Identifying Complementary and Supplementary Angles OMP and PMQ Since 60° + 30° = 90°, PMQ and OMP are complementary. O N P Q R M 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°.

Classifying Angles 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°. Reading Math

Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2B: Identifying Complementary and Supplementary Angles NMO and OMR mNMO = 15° and mOMR = 165° O N P Q R M Since 15° + 165° = 180°, NMO and OMR are supplementary. Read mNMO as “the measure of angle NMO.” Reading Math

Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2C: Identifying Complementary and Supplementary Angles PMQ and QMR O N P Q R M Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary. 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°.

Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2A BAC and CAF mBAC = 35° and mCAF = 145° C B D E F A Since 35° + 145° = 180°, BAC and CAF are supplementary.

Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2B CAD and EAF Since 55° + 35° = 90°, CAD and EAF are complementary. C B D E F A 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°.

Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2C BAC and EAF mBAC = 35° and mEAF = 35° C B D E F A Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary.

Classifying Angles Angles A and B are complementary. If mA is 56 °, what is the mB? Additional Example 3: Finding Angle Measures Since A and B are complementary, mA + mB = 90 °. mA + mB = 90 ° 56 ° + mB = 90 ° – 56 ° mB = 34 ° Substitute 56° for mA. Subtract 56° from both sides. The measure of B = 34 °.

Classifying Angles Angles P and Q are supplementary. If mP is 32 °, what is the mQ? Check It Out: Example 3 Since P and Q are supplementary, mP + mQ = 180 °. mP + mQ = 180 ° 32 ° + mQ = 180 ° – 32 ° mQ = 148 ° Substitute 32° for mP. Subtract 32° from both sides.. The measure of Q = 148 °.

Classifying Angles Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

Classifying Angles Lesson Quiz: Part I Tell whether each angle is acute, right, obtuse, or straight. 1. straight obtuse 2.

Classifying Angles 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M is 117°, what is mN? 63°

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

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

Classifying Angles 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 Lesson Quiz for Student Response Systems

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