We are given four angles and we are asked to find which angle does not belong with the other three. Let's draw each given angle in standard position.

We begin by placing the initial side of the angle in the

x -

axis. Since this is a negative angle, we will move clockwise.

Notice that this angle is greater than

36 0^{\circ} .

We can find angles coterminal to this by adding or subtracting

36 0^{\circ} .

Since it is easier to draw angles with a measure between

0^{\circ}

and

36 0^{\circ},

we will subtract

36 0^{\circ}

from

45 0^{\circ} .

45 0^{\circ} - 36 0^{\circ} = 9 0^{\circ}

This means that this angle is coterminal to an angle of

9 0^{\circ} .

We start by placing the initial side of the angle in the

x -

axis. This time we will move counter-clockwise because this is a positive angle.

Finally, we draw this angle keeping in mind that it is negative. This means that we will move clockwise.

We found that the following angles are coterminal.

45 0^{\circ}, 9 0^{\circ}, - 27 0^{\circ}

Therefore, the angle of

- 9 0^{\circ}

does not belong with the other three.

Exercise