Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 2 - Section 2.6 - Problem Solving in Geometry - Exercise Set - Page 181: 80

Answer

We know that the total of the measures of the angles in a triangle must equal 180°, so if the angles do not add up to 180°, then the three angles cannot form a triangle. Let's add 37°, 58°, and 86° together to see: $$37° + 58° + 86°$$ Let's add the first two angles together: $$95° + 86°$$ Now add this total to 86° to the sum of the first two angles: $$95° + 86° = 181°$$ The sum of these angles is equal to 181°, which we cannot have because the sum of a triangle's angles cannot be any more or any less than 180°. Therefore, this statement does not make sense.

Work Step by Step

We know that the total of the measures of the angles in a triangle must equal 180°, so if the angles do not add up to 180°, then the three angles cannot form a triangle. Let's add 37°, 58°, and 86° together to see: $$37° + 58° + 86°$$ Let's add the first two angles together: $$95° + 86°$$ Now add this total to 86° to the sum of the first two angles: $$95° + 86° = 181°$$ The sum of these angles is equal to 181°, which we cannot have because the sum of a triangle's angles cannot be any more or any less than 180°. Therefore, this statement does not make sense.
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