Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - 5-6 Inequalities in One Triangle - Practice and Problem-Solving Exercises - Page 328: 7


According to the Corollary to the Triangle Exterior Angle Theorem, an exterior angle has a measure that is greater than each of the interior angles that is farthest away from it. In this exercise, $\angle 1$ is an exterior angle; therefore $m \angle 1$ is greater than $m \angle 2$ and $m \angle 1$ is greater than $m \angle 4$ because they are the interior angles of the triangle that are farthest away from the exterior angle.

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