Video: Finding the Reference Angle for a Given Angle

What is the reference angle for 153°?

01:22

Video Transcript

What is the reference angle for 153 degrees?

The reference angle is the positive acute angle using the 𝑥-axis as its frame of reference. Considering the four quadrants as shown in the diagram, where quadrant one is between zero and 90 degrees, quadrant two between 90 and 180 degrees, quadrant three between 180 and 270 degrees, and quadrant four between 270 and 360 degrees, then 153 degrees will be in quadrant two.

If we let the reference angle equal 𝜃, then 𝜃 plus 153 is equal to 180. Subtracting 153 from both sides of this equation gives us a value of 𝜃 of 27 degrees. Therefore, the reference angle for 153 degrees is 27 degrees. We can go one step further that if our angle is in quadrant two, then the reference angle will always be 180 degrees minus this angle.

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