Question

How do you find the reference angle for the angle $ 69^\circ $ ?

Answer 1

Hint: In this question, we have to find the reference angle for the given angle. For that, we must know what reference angle actually is. A reference angle is an angle whose terminal side is in the second, third or fourth quadrant. A reference angle is always smaller than 90 degrees, that is, it is an acute angle.

Complete step-by-step answer:
The initial side of a reference angle is on the positive x-axis and the terminal side is in the first quadrant. So to find the reference angle of any angle, we have to first identify the quadrant in which the angle lies then do some arithmetic operations to find its reference angle.
We know that the reference angle is acute and always lies in the first quadrant. 69 degrees is smaller than 90 degrees, so it is an acute angle and lies in the first quadrant.
Hence the reference angle for the angle $ 69^\circ $ is $ 69^\circ $ .
So, the correct answer is “ $ 69^\circ $ ”.

Note: To find the reference angle of a negative angle, we have to first convert it to a positive angle by adding it to the complete angle $ (360^\circ ) $ , then we will identify the quadrant in which the angle lies. Each quadrant is of 90 degrees, so if an angle lies in the second quadrant then we subtract 90 degrees from it. If the angle lies in the third quadrant then we subtract 180 degrees from it, and if the angle lies in the fourth quadrant then we subtract 270 degrees from it.