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sqdancefan

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Answer:

  • x = 108
  • y = 72
  • z = 18

Step-by-step explanation:

The angles of a linear pair are supplementary. That is, they total 180°. The angle marked x° and the one marked 72° are a linear pair:

  x° +72° = 180°

  x = 180 -72 = 108 . . . . . . . divide by °, subtract 72

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Vertical angles are congruent. Angles y° and 72° are vertical angles, so ...

  y = 72

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Angles z° and 72° together make a right, which has a measure of 90°.

  z° +72° = 90°

  z = 90 -72 = 18 . . . . . . . divide by °, subtract 72

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  (x, y, z) = (108, 72, 18)

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Additional comment

Angles 72° and x° form a linear pair, as do angles x° and y°. That is, angles 72° and y° are both supplementary to angle x°. Angles that are supplementary to the same angle are congruent. This will be the case for any vertical angles: they are supplementary to the same angle.

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