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

Learn to identify angles and angle pairs. Course Classifying Angles M7A1.a Translate verbal phrases to algebraic expressions; M7A2.a Given a problem, define a variable, write an equation, solve the equation, and interpret the solution; M7A2.b Use the addition and multiplication properties of equality to solve one- and two-step linear equations;

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

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

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

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

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2A: Identifying Complementary and Supplementary Angles Course Classifying 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°.

Course 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

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2B: Identifying Complementary and Supplementary Angles Course Classifying 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

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2C: Identifying Complementary and Supplementary Angles Course Classifying Angles PMQ and QMR O N P Q R M Since 30° + 75° = 105°, PMQ and QMR are neither complementary or 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°.

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2A Course Classifying Angles 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.

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2B Course Classifying Angles 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°.

Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out: Example 2C Course Classifying Angles 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 or complementary.

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 °. Course Classifying Angles mA + mB = 90 ° 56 ° + mB = 90 ° – 56 ° mB = 34 ° Substitute 56° for mA. Subtract 56° from both sides to isolate mB. The measure of B = 34 °.

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 complementary, mP + mQ = 180 °. Course Classifying Angles mP + mQ = 180 ° 32 ° + mQ = 180 ° – 32 ° mQ = 148 ° Substitute 32° for mP. Subtract 32° from both sides to isolate mQ. The measure of Q = 148 °.

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

Lesson Quiz: Part II Use the diagram to tell whether the angles are complementary, supplementary, or neither. Insert Lesson Title Here 3. AZB and BZC neither Course Classifying Angles 4. BZC and CZD complementary 5. Angles M and N are supplementary. If M is 117°, what is mN? 63°