Question

Find the measure of the reference angle for each given angle. Part 2

13. θ = -160°
14. θ = 345°
15. θ = =130°

Answer 1

13. 20°

14. 15°

15. 50°

Explanation:

From a mathematical point of view, the reference angle is the smaller of α and (180°-α), where α = θ mod 180°.

That is, add or subtract multiples of 180° until the result is in the range 0–180°. Then choose the smaller of the angle and its supplement.

It is convenient to let a spreadsheet calculate these when you have a bunch of them.

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From a geometrical point of view, the reference angle is the positive angle between the terminal ray and the nearest x-axis.

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For the angles here, the reference angles (in degrees) are shown in the attachment.

Answer 2

13. 20°

14. 15°

15. 50°

Explanation:

Please see the attached pictures for full solution.

For negative angles, the arrow turns clockwise.