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NAME ________________________________________ DATE ______________ PERIOD _____ 10-1 Study Guide and Intervention Angle Relationships • An angle has two sides that share a common endpoint. The point where the sides meet is called the vertex. Angles are measured in degrees, where 1 degree is one of 360 equal parts of a circle. • Angles are classified according to their measure. Right Angle Acute Angle Obtuse Angle Straight Angle • Two angles are vertical if they are opposite angles formed by the intersection of two lines. • Two angles are adjacent if they share a common vertex, a common side, and do not overlap. 4 1 2 3 5 !1 and !3 are vertical angles. !4 and !2 are vertical angles. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. A. C. Classify each angle as acute, obtuse, right, or straight. The angle is less than 90°, so it is an acute angle. Example 2 1 2 !5 and !6 are adjacent angles B. The angle is greater than 90°, so it is an obtuse angle. Label the two angles vertical or adjacent. These angles are vertical because they are opposite each other and formed by two intersecting lines. D. 3 4 These angles are adjacent because they share a common vertex, a common side, and do not overlap. Exercises Classify each angle as acute, obtuse, right, or straight. 1. 2. 3. 4. 7. 8. Label the angles vertical or adjacent. 5. 6. 3 1 2 Chapter 10 6 4 5 151 7 8 Course 2 Lesson 10-1 Example 1 6 NAME ________________________________________ DATE ______________ PERIOD _____ 10-2 Study Guide and Intervention Complementary and Supplementary Angles • Two angles are complementary if the sum of their measure is 90°. m!1 ! m!2 " 90° 1 2 • Two angles are supplementary if the sum of their measure is 180°. 3 m!3 ! m!4 " 180° 4 • To find a missing angle measure, first determine if the angles are complementary or supplementary. Then write an equation and subtract to find the missing measure. Example 1 Find the value of x. The two angles form a right angle or 90°, so they are complementary, 43 ! x " 90 Write the equation. # 43 # 43 Subtract 43 from each side. x " 47 43° x° Example 2 Find the value of x. The two angles form a straight line or 180°, so they are supplementary, 110 ! x " 180 Write the equation. # 110 # 110 Subtract 110 from each side. x " 70 110˚ x˚ so the value of x is 70°. Lesson 10-2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. so the value of x is 47°. Exercises Find the value of x in each figure. 2. 1. 58° x ° 4. 3. 85° 56° x° 5. 71° Chapter 10 x° 6. x° x° 45° 82° x ° 153 Course 2