Question

Determine the complement and/or supplement of each angle. If it is not possible, explain.

Answer 1

Answer:

• complement: 32.8°
• supplement: 122.8°

Step-by-step explanation:

The sum of an angle A and its complement C is 90°:

  A + C = 90°

  C = 90° -A . . . . . subtract A from both sides.

That is, the complement of an angle is found by subtracting the angle from 90°.

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The sum of an angle and its supplement is 180°. This means the supplement of an angle is found by subtracting the angle from 180°. You may notice the supplement is 90° more than the complement.

  A + S = 180°

  S = 180° -A = 90° +(90° -A)

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For the given angle, the complement is ...

  C = 90° -57.2° = 32.8°

And the supplement is ...

  S = 180° -57.2° = 122.8°

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Additional comment

We generally like angle measures to be positive (as with all measures in geometry). Hence, we might say that the complement of an angle greater than 90° does not exist. YMMV