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°.
