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Which set of degrees can be the measures of angles in a triangle? Select all that apply.

32, 84, 64
115, 40, 25
90, 27, 100

1 answer

To determine whether a set of degrees can be the measures of angles in a triangle, we need to check two conditions:

  1. The sum of the angles must equal 180 degrees.
  2. Each angle must be greater than 0 degrees.

Let's evaluate each set of angles:

  1. 32, 84, 64:

    • Sum: 32 + 84 + 64 = 180 degrees (valid)
    • All angles are greater than 0 (valid)
    • This set is valid.

  2. 115, 40, 25:

    • Sum: 115 + 40 + 25 = 180 degrees (valid)
    • All angles are greater than 0 (valid)
    • This set is valid.

  3. 90, 27, 100:

    • Sum: 90 + 27 + 100 = 217 degrees (invalid)
    • Although all angles are greater than 0, the sum exceeds 180 degrees.
    • This set is not valid.

Based on this analysis, the valid sets of angles that can be measures of angles in a triangle are:

  • 32, 84, 64
  • 115, 40, 25