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

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 furthest away from it. In this exercise, $\angle 1$ is an exterior angle; therefore $m \angle 1$ is greater than $m \angle 3$, and $m \angle 1$ is greater than $m \angle 4$. Since $m \angle 2$ is equal to $m \angle 1$ because they are vertical angles, by association, $m \angle 1$ is also greater than $m \angle 2$.

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 are furthest away from it. In this exercise, $\angle 1$ is an exterior angle; therefore $m \angle 1$ is greater than $m \angle 3$ and $m \angle 1$ is greater than $m \angle 4$. Since $m \angle 2$ is equal to $m \angle 1$ because they are vertical angles, by association, $m \angle 1$ is also greater than $m \angle 2$.