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bernardchan

Answer:

1) LInear Pair

2) Adjacent (but not a linear pair)

3) Complementary Angles

4) Vertical angles

Step-by-step explanation:

1st pair of angles are linear because they sum to 180 and are on the same line

2nd pair of angles are adjacent but not linear because they're not on a line

3rd pair of angles are complementary because they're neighboring a 90° angle and the three angles share the same line.

4th pair of angles are vertical because they're across from each other.

Answers:

  1. Linear Pair
  2. Adjacent (but not a linear pair)
  3. Complementary
  4. Vertical Angles

The answers are given from top to bottom in that exact order.

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Explanations:

  1. Angles AOB and DOB are considered a linear pair because they are adjacent and supplementary. They are adjacent because they share a common wall so to speak. That wall being ray OB. They are supplementary because they form a 180 degree angle. As the name "linear pair" implies, the pair of angles form a straight line.
  2. Unlike the previous set of angles, these angles are not supplementary. So they aren't a linear pair. However, the angles do share a common ray. So they are adjacent.
  3. These angles combine to a right angle (aka 90 degrees). Therefore, they are complementary angles that form a sharp corner.
  4. These are vertical angles because they are opposite one another. Ignore ray OB and only focus on lines AD and EC. Vertical angles form whenever we have this X shape like this, and the vertical angles are opposite one another. Vertical angles are always congruent.

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