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

8-2 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

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

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

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

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

8-2 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°.

8-2 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

8-2 Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2C: Identifying Complementary and Supplementary Angles 8-2 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°.

8-2 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.

8-2 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°.

8-2 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.

8-2 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 °.

8-2 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 °.

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

8-2 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°