Final answer:
If the question provides the angles of a triangle as 30°, 60°, and 90°, or 45°, 45°, and 90°, we are dealing with a right triangle. Depending on the measures of the angles, the triangle can be classified as either a 30-60-90 triangle or a 45-45-90 isosceles right triangle. Without sufficient information, the exact measures of the angles cannot be determined.
Step-by-step explanation:
When considering a triangle with angle measures provided as options, we recall the fundamental property that the sum of internal angles in any triangle is 180 degrees. The question presents three possible sets of angle measures:
- 30°, 60°, and 90°
- 45°, 45°, and 90°
- A 90° angle, with unspecified other angles
Both of the first two options include a 90° angle, indicating that we are dealing with a right triangle. Right triangles have specific properties and can be classified as either 30-60-90 or 45-45-90 triangles, depending on the measures of the other two angles. A 30-60-90 triangle has angles in the ratio of 1:2:√3, and a 45-45-90 triangle, also called an isosceles right triangle, has two angles of 45° each. The third option implies insufficient information to determine the exact measures of all angles.