# Precalculus : Find the Degree Measure of an Angle

## Example Questions

### Example Question #71 : Trigonometric Functions

Convert radians to degrees.      Explanation:

Write the conversion factor between radians and degrees. Cancel the radians unit by using dimensional analysis. ### Example Question #1 : Angles In The Coordinate Plane

Convert to degrees.      Explanation:

Write the conversion factor of radians and degrees. Substitute the degree measure into . ### Example Question #1 : 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 #2 : Find The Degree Measure Of An Angle

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 #3 : 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: ### All Precalculus Resources 