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Learn to identify angles and angle pairs. Vocabulary. angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles. A. Vertex. 1. B. C.
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Vocabulary angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles
A Vertex 1 B C An angleis 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 (°).
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°. Anobtuse angle is an angle that measures more than 90° but less than 180°. A straightangle is an angle that measures exactly 180°.
Additional Example 1: Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. B. acute angle obtuse angle
Reading Math You can name this angle ABC, CBA, B, or 1. A • 1 B• •C
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.
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mOMP = 60°. P Q O N R M Additional Example 2A: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ Since 60° + 30° = 90°, PMQ andOMP are complementary.
Reading Math 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°.
P Q Reading Math O Read mNMO as “the measure of angle NMO.” N R M 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 andOMR are supplementary.
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mQMR = 75°. P Q O N R M 8-2 Additional Example 2C: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. PMQ and QMR Since 30° + 75° = 105°, PMQ andQMR are neither complementary nor supplementary.
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° Substitute 56° for mA. Subtract 56° from both sides. – 56° – 56° mB = 34° The measure of B = 34°.
Lesson Quiz for Student Response Systems • 1. Identify the type of the given angle. A. acute B. obtuse C. right D. straight
Lesson Quiz for Student Response Systems • 2. Identify the type of the given angle. A. acute B. obtuse C. right D. straight
Lesson Quiz for Student Response Systems • 3. Use the diagram to identify the type of the given pair of angles. mAOB and mBOD A. complementary B. supplementary C. right D. none
Lesson Quiz for Student Response Systems • 4. Angles A and B are complementary. If mA is 36°, what is mB? A.54° B.90° C.126° D.144°