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

Angles are measured in degrees (°). 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 (°).

You can name this angle ABC, CBA, B, or 1. Reading Math

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°.

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.

Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary

The sum of the measures of the angles in a triangle is 180°. Angles of a Triangle The sum of the measures of the angles in a triangle is 180°. m1 + m2 + m3 = 180° 2 1 3

Additional Example 1: Finding an Angle Measure of in a Triangle 55° Find the measure of the unknown angle. 80° x The sum of the measures of the angles is 180°. 80° + 55° + x = 180° 135° + x = 180° Combine like terms. –135° –135° Subtract 135° from both sides. x = 45° The measure of the unknown angle is 45°.

Check It Out: Example 1 30° Find the measure of the unknown angle. 90° x The sum of the measures of the angles is 180°. 90° + 30° + x = 180° 120° + x = 180° Combine like terms. –120° –120° Subtract 120° from both sides. x = 60° The measure of the unknown angle is 60°.

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

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

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.

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

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

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.