# Precalculus : Find the Degree Measure of an Angle

## Example Questions

### Example Question #1 : Angles In The Coordinate Plane

Explanation:

Write the conversion factor between radians and degrees.

Cancel the radians unit by using dimensional analysis.

### Example Question #2 : Angles In The Coordinate Plane

Convert  to degrees.

Explanation:

Write the conversion factor of radians and degrees.

Substitute the degree measure into .

### Example Question #3 : Find The Degree Measure Of An Angle

Determine the angle  in degres made in the plane by connecting a line segment from the origin to .

Assume

Explanation:

Firstly, since the point  is in the 3rd quadrant, it'll be between  and . If we take  to be the horizontal, we can form a triangle with base and leg of values  and . Solving for the angle in the 3rd quadrant given by

Since this angle is made by assuming  to be the horizontal, the total angle measure  is going to be:

### Example Question #4 : Angles In The Coordinate Plane

Find the degree measure of  radians.  Round to the nearest integer.

Explanation:

In order to solve for the degree measure from radians, replace the  radians with 180 degrees.

The nearest degree is .

### Example Question #4 : Find The Degree Measure Of An Angle

Given a triangle, the first angle is three times the value of the second angle.  The third angle is .  What is the value of the second largest angle in degrees?

Explanation:

A triangle has three angles that will add up to  degrees.

Convert the radians angle to degrees by substituting  for every .

The third angle is 60 degrees.

Let the second angle be .  The first angle three times the value of the second angle is .  Set up an equation that sums the three angles to .

Solve for .

Substitute  for the first angle and second angle.

The second angle is:

The first angle is:

The three angles are:

The second highest angle is: