Question

What do you find the reference angle for the angle $ - {126^{\circ}}$.

Answer 1

Hint: In order to solve this question we will have to find the quadrant where this angle lies in the four-quadrant. Since it is negative so we will have to add it from a complete angle then for finding the reference we will subtract the resultant from the straight angle, and that will be the final answer.

Complete step by step Solution:
For solving this question we want the exact position of the quadrant where this angle lies, as the angle which is given in the question to us is negative we will add this by a complete angle so that it may move the whole one round and the exact quadrant may be found.
$ - {126^{\circ}} + {360^{\circ}} = {234^{\circ}}$
Now as the range of the third quadrant is from ${180^{\circ}}$ to ${270^{\circ}}$ so this will lie in the first quadrant.
Now for finding the reference we will have to subtract it from the ${180^{\circ}}$.

${234^{\circ}} - {180^{\circ}} = {54^{\circ}}$
So this will be our final answer.

Additional information:
An angle with a terminal side in the second, third, or fourth quadrant has what we call a reference angle in the first quadrant. A reference angle is an acute angle, measuring less than ${90^{\circ}}$, that has its initial side on the positive x-axis and terminal side in the first quadrant.

Note:
While solving these types of questions we should also analyze by our imagining power that if the angle is negative then up to where it will go in the negative side as all the quadrants we know are of ${90^{\circ}}$ each.
Or we can go by the negative as count it as positive for finding the accurate position of the angle.