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Name Class Date Lesson 6-1 Angle Measures Lesson Objective Common Core Standard To write and solve equations to find unknown angle measures Geometry: 7.G.5 Vocabulary An angle is a figure formed by two rays with a common endpoint. All rights reserved. angle between 0 ° and 90 ° right obtuse angle angle between 90 ° and 180 90 ° straight ° that share a vertex and a side Adjacent angles are angles 180 ° Circle an angle adjacent to 1. but have no interior points in common. congruent angles formed by two Vertical angles are the 4 intersecting lines and are opposite each other. 1 3 2 2 or 4 Circle an vertical angle to 1. 1 4 2 3 If the sum of the measure of two angles is 90°, the angles are complementary . If the sum is 180°, the angles are supplementary . 3 39 ° 51° angle complementary 65° 115 ° supplementary Congruent angles are angles with equal measures. © Pearson Education, Inc., publishing as Pearson Prentice Hall. acute 64 441197_C2_Ch6_WKbk_Ver-1.indd 64 Course 2 Lesson 6-1 Daily Notetaking Guide 10/10/12 2:20 PM Name Class Date Examples 1 Finding Supplements and Complements Write and solve an equation to find the measures of the two angles described at the right. 6x 1 (19x 1 5) 5 180 1 d The angles are supplementary. 2 6x 1 19x 1 5 5 180 d Use the Associative Property. 25x 1 5 5 180 d Combine like terms. 19x 5° 6x All rights reserved. 25x 1 5 2 5 5 180 2 5 d Subtract 5 from each side. 25x 5 175 25x 25 5 175 25 x 5 7 d Simplify. d Divide. d Simplify. Calculate the angle measures. 6 7 5 42 and 19 7 1 5 5 138 The angle measures are 42 ° and 138 °. 2 Finding Angle Measures In the diagram, m3 5 32°. © Pearson Education, Inc., publishing as Pearson Prentice Hall. Find the measures of 1, 2, and 4. m2 1 32° 5 180° d &2 and &3 are 1 supplementary . 2 4 3 m2 1 32° 2 32° 5 180° 2 32°d Subtract 32° from each side. m2 5 148° d Simplify. m1 5 32° d &1 and &3 are vertical angles. m4 5 148° d &2 and &4 are vertical angles. Quick Check 1. Write and solve an equation to find the measures of the two angles described at the right. 65°; 115° (13x)° (11x 60)° 2. In the diagram at the right, m8 5 72°. Find the measures of 5, 6, and 7. 108°; 72°; 108° Daily Notetaking Guide 441197_C2_Ch6_WKbk_Ver-1.indd 65 8 5 7 6 Course 2 Lesson 6-1 65 10/10/12 2:20 PM