An angle has a reference angle measuring 35º and its terminal side lies in Quadrant IV. What are possible positive and negative measures for the angle?

This question is based on concept of reference angle.Therefore, the positive measures for the angle would be 35° and the negative would be 325°.

Given:

The reference angle is 35º and its terminal side lies in Quadrant .

By the definition of reference angle,

An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.

Thus, positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.

The reference angle is acute angle.Therefore, it must be < 90°.

In radian measure, it must be less than  .

Therefore, the reference angle is less than 35°. So, reference angle is positive.And the negative angle is 360 - 35 = 325°.

Therefore, the positive measures for the angle would be 35° and the negative would be 325°.

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Step-by-step explanation:

Given that,

The reference angle is 35°

It lies in the fourth quadrant.

The reference angle is the positive acute angle that can represent an angle of any measure.

The reference angle  must be < 90∘.

In radian measure, the reference angle  must be < π/ 2.

Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.

Since the reference angle is less than 35°, then, the reference angle is positive,

The negative angle is 360 - 35 = 325°

So, the positive reference angle is 35° and the negative reference angle is 325°