Question

How do you find the reference angle for angle 275 degrees?

Answer 1

Hint: The reference angle is the angle between ray and positive x axis or negative x axis depending upon the quadrant. If the angle is in the first or fourth quadrant it will be measured with a positive x axis and if the angle is in the second or fourth quadrant it will be measured from the negative x axis.

Complete step by step answer:
We have to find the reference angle for angle 275 degrees first we have to find in which quadrant 275 degrees lies.
For different quadrants there is a different formula for reference angle.
For first quadrant for angle x
  

If the angle in the first quadrant is the reference angle taken from the positive x axis so that is equal to value of angle.
Reference angle= ${{x}^{\circ }}$
If the angle lie in second quadrant

The angle shown as ${{180}^{\circ }}-{{x}^{\circ }}$ is the reference angle if angle will lie on the second quadrant then angle measure from negative x axis is reference angle.
Reference angle= ${{180}^{\circ }}-{{x}^{\circ }}$
If the angle lie in third quadrant

The angle shown as ${{x}^{\circ }}-{{180}^{\circ }}$ is the reference angle if angle will lie on the third quadrant then angle measure from the negative x axis is reference angle.
Reference angle= ${{x}^{\circ }}-{{180}^{\circ }}$
If the angle lie in fourth quadrant

The angle shown in red is the reference angle if angle will lie on the fourth quadrant then angle measure from the positive x axis is reference angle.
Reference angle= ${{360}^{\circ }}-{{x}^{\circ }}$
${{275}^{\circ }}$ lie in fourth quadrant so the reference angle= ${{360}^{\circ }}-{{275}^{\circ }}={{85}^{\circ }}$

Note:
To find out the reference angle we need to know in which quadrant the angle lies, then we can find the reference angle by graph or formula. If the angle is between 1 to 90 degrees it is in the first quadrant, if the angle is between 90 to 180 degrees it is in the second quadrant, 180 to 270 degrees third and 270 to 360 degrees fourth quadrant.