Chapter 2.5, Problem 28WE

To determine

To conclude: The angles $\angle 3$ and $\angle 1$ are complementary.

Answer to Problem 28WE

The angles $\angle 3$ and $\angle 1$ are complementary

Explanation of Solution

Given information:

  

  $\overrightarrow{AO}\perp \overrightarrow{CO}$

Since $\overrightarrow{AO}\perp \overrightarrow{CO}$

If the lines are perpendicular then the angle made by them is right angle

Thus,

  $\angle AOC={90}^{\circ }$ or $\angle 2+\angle 1={90}^{\circ }$

When two lines are cut by the transversal then the angle made by them are called vertically opposite angles.

The angles and $\angle 3$ are vertically opposite angle

Thus,

  $\angle 2=\angle 3$

Therefore, $\angle 3+\angle 1={90}^{\circ }$ and therefore $\angle 3$ and $\angle 1$ are complementary.