Equivalent Angles

They are angles within different quadrants with the same value or magnitude. They can be negative or positive or acute, obtuse or reflex. For angles that are greater or negative than 360o, they can be solved using subtracting 360o when it is greater or by adding 360o if it’s negative..

Table of Contents

Example 1

Based on the angles listed below:

(i). Determine (i). Decide the quadrant(ii). Declarate its equivalent if applicable.

(a) 288o

(b) -293o

(c) 191o

(d) 167o

(e) 635o

(f) 490o

(g) -610o


(ai) 288o – 4th quadrant

(aii) 288o = -72o

(bi) (bi) than 0o, therefore we will add 360o

-293o + 360o = 67o

-293o – 1st quadrant

(bii) -293o = 67o

(ci) 191o – 3rd quadrant

(cii) 191o = -169o

(di) 167o = 2nd quadrant

(dii) 167o = -193o

(ei) (ei) 630o is higher than 360o, so we subtract 360o

635o – 360 = 275o

4th quadrant

(eii) 630o = 275o

(fi) 490o – 2nd quadrant

(fii) 490o = 130o

(gi) (gi) than 0o. Therefore, we will add 360o

-610o + 360o = -250o

It’s not quite zero, which is why we need to add 360.

-250o + 360o = 110o

-610o 2nd quadrant

(gii) -610o = 110o

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