Chapter 13, Problem 9E

Solution

To find: The measure of angle shown below in standard position.

  

The measure of angle in standard position is $135°\text{ or }-225°$ .

Given:

The angle is shown below.

  

Concept used:

An angle in the coordinate plane is in standard position when the vertex is at the origin and one ray is on the positive $x-$ axis. The ray on positive $x-$ axis is initial side of the angle whereas the other side is the terminal side of the angle. The measure of angle in standard position is the amount of rotation from initial side to the terminal side.

Calculation:

From the figure shown of the angle in standard position it can be interpreted that the vertex is at origin and one ray is on the negative $x-$ axis. And the terminal side of the angle makes a clockwise rotation of $180°+45°=225°$ and due to clockwise rotation of angle, the angle $225°$ is negative. Hence the measure of angle is $-225°$ .

And if we measure the angle anticlockwise, the measure of angle in standard position is $90°+45°=135°$ .

Conclusion:

The measure of angle in standard position is $135°\text{ or }-225°$ .