Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 6 - Polygons and Quadrilaterals - Common Core Cumulative Standards Review - Selected Response - Page 427: 10



Work Step by Step

The sum of the interior angles of any triangle must equal $180^{\circ}$, no more and no less. Option $F$ is incorrect. If two right angles are in the triangle, then those two angles would add up to $180^{\circ}$ already, which is what all the interior angles of a triangle should equal. The third angle cannot equal $0^{\circ}$. Option $G$ is correct. If one of the angles in the triangle is obtuse, there is only room for two acute angles. We cannot have another obtuse angle or even a right angle because the sum of the three angles would equal more than $180^{\circ}$. Option $H$ is incorrect. Two obtuse angles in one triangle would already have a sum of greater than $180^{\circ}$. The third angle cannot be negative. Option $I$ is incorrect. There are no vertical angles in a triangle.
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