## Elementary Geometry for College Students (6th Edition)

The sum of the angles 1 and 4 must be $90^{\circ}$. By definition, this means that angles 1 and 4 are complementary.
Since AB is a straight line, the angle $\angle AOB$ is equal to $180^{\circ}$ When $\angle AOB$ is subdivided into a certain number of angles, the sum of these angles must be $180^{\circ}$ Since angles 2 and 3 are complementary, the sum of these two angles is $90^{\circ}$ Then the sum of the angles 1 and 4 must also be $90^{\circ}$. By definition, this means that angles 1 and 4 are complementary.