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What is a Reference Angle?

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Rules of Angles and Reference angle


Positive angles go in a counter clockwise direction. Below is a picture of a positive fifty degree angle
Quadrant I
Every positive angle in quadrant I is already acute...so the reference angle is the measure of the angle itself:

Quadrant II
To find the reference angle measuring x ° for angle in Quadrant III, the formula is $$ 180 - x^{\circ} $$ .
quadrant II general pic

Quadrant III
To find the reference angle measuring x ° for angle in Quadrant III, the formula is $$ x - 180 ^{\circ} $$ .
quadrant II general pic

Quadrant IV
To find the reference angle measuring x ° for angle in Quadrant IV, the formula is $$360 ^{\circ} -x $$ .
quadrant II general pic
What is the reference angle for the angle in the graph below?
Answer

What is the reference angle for a 210° angle?
Answer



What is the reference angle for a 300° angle?
Answer

Word Problems


Problem 1) What is the reference angle for an angle that measures 91 ° ?
Answer


Problem 2) What is the reference angle for an angle that measures 250 ° ?
Answer


Further Reading