Question
Which set of angle measures could be the interior angles of a triangle?
A. 90∘ ,90∘ ,90∘
B. 80∘, 80∘ ,200∘
C. 40∘, 50∘, 60∘
D. 15∘, 30∘, 135∘
A. 90∘ ,90∘ ,90∘
B. 80∘, 80∘ ,200∘
C. 40∘, 50∘, 60∘
D. 15∘, 30∘, 135∘
Answers
GPT-4o mini
To determine which set of angle measures could be the interior angles of a triangle, we need to remember that the sum of the interior angles of a triangle must equal 180 degrees. Additionally, each individual angle must be greater than 0 degrees.
Let's analyze the options:
A. \(90^\circ, 90^\circ, 90^\circ\)
- Sum: \(90 + 90 + 90 = 270^\circ\) (not valid)
B. \(80^\circ, 80^\circ, 200^\circ\)
- Sum: \(80 + 80 + 200 = 360^\circ\) (not valid)
C. \(40^\circ, 50^\circ, 60^\circ\)
- Sum: \(40 + 50 + 60 = 150^\circ\) (not valid)
D. \(15^\circ, 30^\circ, 135^\circ\)
- Sum: \(15 + 30 + 135 = 180^\circ\) (valid)
Only option D has angles that both sum to 180 degrees and are all greater than 0 degrees.
Thus, the set of angle measures that could be the interior angles of a triangle is **D. \(15^\circ, 30^\circ, 135^\circ\)**.
Let's analyze the options:
A. \(90^\circ, 90^\circ, 90^\circ\)
- Sum: \(90 + 90 + 90 = 270^\circ\) (not valid)
B. \(80^\circ, 80^\circ, 200^\circ\)
- Sum: \(80 + 80 + 200 = 360^\circ\) (not valid)
C. \(40^\circ, 50^\circ, 60^\circ\)
- Sum: \(40 + 50 + 60 = 150^\circ\) (not valid)
D. \(15^\circ, 30^\circ, 135^\circ\)
- Sum: \(15 + 30 + 135 = 180^\circ\) (valid)
Only option D has angles that both sum to 180 degrees and are all greater than 0 degrees.
Thus, the set of angle measures that could be the interior angles of a triangle is **D. \(15^\circ, 30^\circ, 135^\circ\)**.