Which angles are linear pairs? check all that apply. ∠srt and ∠trv ∠srt and ∠tru ∠vrw and ∠wrs ∠vru and ∠urs ∠urw and ∠wrs

General
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which angles are linear pairs? check all that apply. ∠srt and ∠trv ∠srt and ∠tru ∠vrw and ∠wrs ∠vru and ∠urs ∠urw and ∠wrs

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Which angles are linear pairs? Check all that apply. ∠srt and ∠trv ∠srt and ∠tru ∠vrw and ∠wrs ∠vru and ∠urs ∠urw and ∠wrs

Answer: To determine which angles are linear pairs, we need to understand that linear pairs are two adjacent angles whose non-common sides form a straight line. In other words, the sum of the measures of a linear pair of angles is 180 degrees.

Let’s analyze each pair of angles given:

  1. ∠srt and ∠trv:

    • If ∠srt and ∠trv share a common side and their non-common sides form a straight line, they are a linear pair.
    • For example, if point T is between points S and V on a straight line, then ∠srt and ∠trv would be linear pairs.

  2. ∠srt and ∠tru:

    • These angles share a common vertex T, but without additional information about their orientation, we cannot confirm they form a straight line.
    • If ∠srt and ∠tru do not form a straight line, they are not a linear pair.

  3. ∠vrw and ∠wrs:

    • If these angles share a common side WR and their non-common sides form a straight line, they are a linear pair.
    • For example, if point R is between points V and S on a straight line, then ∠vrw and ∠wrs would be linear pairs.

  4. ∠vru and ∠urs:

    • Similar to the previous pairs, if these angles share a common side RU and their non-common sides form a straight line, they are a linear pair.
    • For example, if point R is between points V and S on a straight line, then ∠vru and ∠urs would be linear pairs.

  5. ∠urw and ∠wrs:

    • If these angles share a common side WR and their non-common sides form a straight line, they are a linear pair.
    • For example, if point R is between points U and S on a straight line, then ∠urw and ∠wrs would be linear pairs.

Based on this analysis, the angles that are linear pairs are:

  • ∠srt and ∠trv
  • ∠vrw and ∠wrs
  • ∠vru and ∠urs
  • ∠urw and ∠wrs

Therefore, the correct linear pairs are:

  • ∠srt and ∠trv
  • ∠vrw and ∠wrs
  • ∠vru and ∠urs
  • ∠urw and ∠wrs