Find the measure of the reference angle for each given angle. Part 2
13. Θ = -160°
14. Θ = 345°
15. Θ = =130°

13. 20°

14. 15°

15. 50°

Step-by-step explanation:

Please see the attached pictures for full solution.

For negative angles, the arrow turns clockwise.

  13. 20°

  14. 15°

  15. 50°

Step-by-step 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.

angle uzt is congruent to angle tzy. angle vzw is congruent to angle yzx.

(credits to leowren)

step-by-step explanation:

easy math just plug in a and b

step-by-step explanation: