Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 5 - Section 5.1 - Ratios, Rates, and Proportions - Exercises - Page 216: 25

Answer

The angles are: $60^{\circ}, 80^{\circ}, 100^{\circ},$ and $120^{\circ}$

Work Step by Step

Let the angles be $3x, 4x, 5x$ and $6x$ We can find the value of $x$: $3x+4x+5x+6x = 360^{\circ}$ $18x = 360^{\circ}$ $x = \frac{360^{\circ}}{18}$ $x = 20^{\circ}$ We can find the four angles: $3x = (3)(20^{\circ}) = 60^{\circ}$ $4x = (4)(20^{\circ}) = 80^{\circ}$ $5x = (5)(20^{\circ}) = 100^{\circ}$ $6x = (6)(20^{\circ}) = 120^{\circ}$ The angles are: $60^{\circ}, 80^{\circ}, 100^{\circ},$ and $120^{\circ}$
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