Elementary Geometry for College Students (7th Edition) Clone

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: 49

Answer

The measure of the interior angle at vertex N is $~190^{\circ}$

Work Step by Step

We can find the value of $y$ by considering the sum of all six interior angles: $y+y+y+y+2(y+10)+2(y+10) = (6-2)~\cdot 180^{\circ}$ $8y+40 = (4)~\cdot 180^{\circ}$ $8y+40 = 720^{\circ}$ $8y = 680^{\circ}$ $y = 85^{\circ}$ We can find the measure of the interior angle at vertex N: $2(y+10) = (2) \cdot (85^{\circ}+10^{\circ}) = 190^{\circ}$
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