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Answer :
To determine which sets of degrees can be the measures of angles in a triangle, you need to check if the sum of the angles in each set is equal to 180 degrees. This is because, in a triangle, the sum of the interior angles must always be 180 degrees. Let's go through each option step-by-step:
1. 16, 87, 87
- Calculate the sum: 16 + 87 + 87 = 190
- Since the sum is not 180, this set cannot be the angles of a triangle.
2. 32, 84, 64
- Calculate the sum: 32 + 84 + 64 = 180
- The sum is 180, so this set can be the angles of a triangle.
3. 143, 66, 161
- Calculate the sum: 143 + 66 + 161 = 370
- Since the sum is not 180, this set cannot be the angles of a triangle.
4. 115, 40, 25
- Calculate the sum: 115 + 40 + 25 = 180
- The sum is 180, so this set can be the angles of a triangle.
5. 90, 27, 100
- Calculate the sum: 90 + 27 + 100 = 217
- Since the sum is not 180, this set cannot be the angles of a triangle.
6. 30, 60, 90
- Calculate the sum: 30 + 60 + 90 = 180
- The sum is 180, so this set can be the angles of a triangle.
Based on these calculations, the sets that can be the measures of angles in a triangle are:
- 32, 84, 64
- 115, 40, 25
- 30, 60, 90
1. 16, 87, 87
- Calculate the sum: 16 + 87 + 87 = 190
- Since the sum is not 180, this set cannot be the angles of a triangle.
2. 32, 84, 64
- Calculate the sum: 32 + 84 + 64 = 180
- The sum is 180, so this set can be the angles of a triangle.
3. 143, 66, 161
- Calculate the sum: 143 + 66 + 161 = 370
- Since the sum is not 180, this set cannot be the angles of a triangle.
4. 115, 40, 25
- Calculate the sum: 115 + 40 + 25 = 180
- The sum is 180, so this set can be the angles of a triangle.
5. 90, 27, 100
- Calculate the sum: 90 + 27 + 100 = 217
- Since the sum is not 180, this set cannot be the angles of a triangle.
6. 30, 60, 90
- Calculate the sum: 30 + 60 + 90 = 180
- The sum is 180, so this set can be the angles of a triangle.
Based on these calculations, the sets that can be the measures of angles in a triangle are:
- 32, 84, 64
- 115, 40, 25
- 30, 60, 90
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