Problem 1176

Find the reference angle for the following angle.





A reference angle for the angle θ is the positive acute angle made by the terminal side of angle θ and the x-axis.

The reference angle of an angle of an angle with measure greater than 360° is found by first finding its coterminal angle that lies between 0° and 360° and then finding the reference the reference angle of the angle.

First, the coterminal angle for 755° lying between 0° and 360° can be found by subtracting 360° twice.

755° – 360° – 360° = 55°

The terminal side of the angle 55° lies in quadrant I since 0° < 55°<90°.

Since the angle is in quadrant I, the angle formed by the x-axis and the specified angle θ is θ itself.

Therefore, the reference angle for 775° is identical to the coterminal angle, 55°.


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