Question

How do you find the reference angle for -225?

Answer 1

Hint : In this question, we are given an angle and we have to find the reference angle for it. For that, we must know what reference angle actually is. A reference angle is always smaller than 90 degrees, that is, it is an acute angle. The initial side of a reference angle is on the positive x-axis and the terminal side is in the first quadrant. The given angle is a negative angle so we will add it to the complete angle $(360^\circ )$ , then we will identify the quadrant in which the angle lies and then do some arithmetic operations to find its reference angle.

Complete step by step solution:
We have to find the reference angle for $- 225^\circ$
So, the positive value of the given negative angle is $360^\circ - 225^\circ = 135^\circ$
This angle is greater than 90 degrees but smaller than 180 degrees, so it lies in the second quadrant.
To find its reference angle, we will subtract 90 degrees from it –
$135^\circ - 90^\circ = 45^\circ$
Hence the reference angle for $- 225^\circ$ is $45^\circ$ .
So, the correct answer is “ $45^\circ$ ”.

Note : We know that each quadrant is 90 degrees. So we subtract 90 degrees from the angle if it lies in the second quadrant. If the angle lies in the third quadrant then we subtract 180 degrees from it, and we subtract 270 degrees from the angle if it lies in the fourth quadrant. Thus, after converting the given negative angle to a positive angle, we identified the quadrant in which the angle lies.