# How do you sketch the angle -240 degrees and find its reference angle?

##### 2 Answers

Add +360 degrees until you have a positive angle, then sketch. The reference angle is the angle from the sketch to the x-axis, in this case, 60 degrees.

#### Explanation:

It makes sense here to state the angle in terms of its positive coterminal angle. To find this, add a positive rotation (360 degrees) until you get a positive angle.

Since 120 is positive, you can stop here. A 120 degree angle is in QII, so that's where you'll draw your sketched angle. The reference angle is the angle that gets you to the x-axis. For an angle of 120 degrees, we would subtract that from 180 degrees to find the reference angle:

Your reference angle is therefore 60 degrees.

The required reference angle is

#### Explanation:

**Given:**

We need to find the **Reference Angle** for this given angle.

We are given

Note that it is a **negative angle**.

To find the **reference angles** we can use the chart below:

The chart given above refers to **positive angles only**.

**Coterminal angles** are **angles in standard position** (angles with the initial side on the **positive x -axis**) that have a **common terminal side. **

Then, we can find the **Coterminal angle** and find the **reference angle** using the chart above.

Please note that the **coterminal angle** and the given **negative angle** in our problem always add up to

So, our coterminal angle can be calculated as follows:

Hence, our coterminal angle =

We will roughly sketch the details as shown below:

**Important:**

We know that the negative angle

Now, we are in a position to find the **reference angle** using the **formula chart**.

The required reference angle is