Question
Which set of angle measures could be the measures of the interior angles of a triangle?
50°, 60°, and 75°
35°, 105°, and 45°
62°, 62°, and 62°
90°, 45°, and 45°
50°, 60°, and 75°
35°, 105°, and 45°
62°, 62°, and 62°
90°, 45°, and 45°
Answers
GPT-4o mini
To determine which set of angle measures could represent the interior angles of a triangle, we need to remember that the sum of the interior angles of a triangle is always 180 degrees.
Let's check each set:
1. **50°, 60°, and 75°**
- Sum = 50 + 60 + 75 = 185° (not a triangle)
2. **35°, 105°, and 45°**
- Sum = 35 + 105 + 45 = 185° (not a triangle)
3. **62°, 62°, and 62°**
- Sum = 62 + 62 + 62 = 186° (not a triangle)
4. **90°, 45°, and 45°**
- Sum = 90 + 45 + 45 = 180° (this is valid for a triangle)
The only set of angle measures that could represent the interior angles of a triangle is **90°, 45°, and 45°**.
Let's check each set:
1. **50°, 60°, and 75°**
- Sum = 50 + 60 + 75 = 185° (not a triangle)
2. **35°, 105°, and 45°**
- Sum = 35 + 105 + 45 = 185° (not a triangle)
3. **62°, 62°, and 62°**
- Sum = 62 + 62 + 62 = 186° (not a triangle)
4. **90°, 45°, and 45°**
- Sum = 90 + 45 + 45 = 180° (this is valid for a triangle)
The only set of angle measures that could represent the interior angles of a triangle is **90°, 45°, and 45°**.