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.

range is infinite on both x and y axis positive and negative

step-by-step explanation:

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x