Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 5 - Section 5.1 - Ratios, Rates, and Proportions - Exercises - Page 227: 24

Answer

Angle 1: 48 Degrees Angle 2: 72 Degrees Angle 3: 96 Degrees Angle 4: 144 Degrees

Work Step by Step

Sum of angles = (# of sides - 2)180 4-2 = 360 Add up the total number of parts within the ration 2 + 3 + 4 + 6 = 15 Divide the total number of degrees in the quadrilateral (360) by the total number of parts in the ratio (15) 360/15 = 24 (1 part in the ratio) Multiply the ratio of one part by the number in each part in the ratio. 24 x 2 = 48 Degrees 24 x 3 = 72 Degrees 24 x 4 = 96 Degrees 24 x 6 = 144 Degrees Add up all four angles to check to see if they equal the sum of angles in a quadrilateral(360) 48 + 72 + 96 + 144 = 360
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