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Tell whether the statement is always, sometimes, or never true. Explain your reasoning.
(a) Complementary angles are adjacent.
(b) Angles in a linear pair are supplements of each other.
(c) Vertical angles are adjacent.
(d) Vertical angles are supplements of each other.
(e) If an angle is acute, then its complement is greater than its supplement.
(f) If two complementary angles are congruent, then the measure of each angle is 45°.

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sqdancefan

Answer:

  • a) sometimes
  • b) always
  • c) never
  • d) sometimes
  • e) never
  • f) always

Step-by-step explanation:

(a) Complementary angles are adjacent. sometimes

  Complementary angles sum to 90°. They don't have to be adjacent.

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(b) Angles in a linear pair are supplements of each other. always

  That the angles are supplementary is part of the definition of a linear pair.

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(c) Vertical angles are adjacent. never

  Vertical angle share a vertex, but not a side. They cannot be adjacent.

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(d) Vertical angles are supplements of each other. sometimes

  Vertical angles are always congruent. If they are both 90°, then they will be supplementary.

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(e) If an angle is acute, then its complement is greater than its supplement. never

  The supplement of an angle is always 90° more than the complement of the same angle. The complement of an angle cannot be greater than its supplement.

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(f) If two complementary angles are congruent, then the measure of each angle is 45°. always

  Complementary angles sum to 90°, so if they have the same measure, that measure must be 45°.