Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 2 - Section 2.5 - Convex Polygons - Exercises - Page 116: 48


The measure of the reflex angle at vertex E is $~216^{\circ}$

Work Step by Step

We can find the value of $x$ by considering the sum of all five interior angles: $x+x+2x+2x+4x = (5-2)~\cdot 180^{\circ}$ $10x = (3)~\cdot 180^{\circ}$ $x = 54^{\circ}$ We can find the measure of the reflex angle: $4x = (4) \cdot (54^{\circ}) = 216^{\circ}$
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