How many triangles can be constructed with angles measuring 25°, 25°, and 130°? A. One B. More than one C. None

C. None

To explain why, let's think about the properties of a triangle. The sum of the internal angles in any triangle is always 180°, no matter what type of triangle it is. This is known as the triangle sum theorem.

If we add up the given angles: 25° + 25° + 130°, the sum is 180°. At first glance, it might seem like it is possible to construct a triangle with these angles. However, there is a problem: the angles given are so specific that there is only one way they can come together to form a triangle. If you were to draw one triangle with these measurements, then every triangle made with these same measurements would be exactly the same as the first, just possibly larger or smaller in scale. This means they would all be congruent or similar: they would all have the same shape, but not necessarily the same size.

However, there is a critical point that actually makes it impossible to construct any triangles with these measurements. The larger angle, which is 130°, is already bigger than any of the two minor angles (25°). In a triangle, an exterior angle is equal to the sum of the two opposite interior angles. In this case, let's say the 130° angle was an exterior angle, this could work because it is the sum of the two 25° angles. But since we are trying to make it an interior angle, the math simply doesn't work out.

In conclusion, since the sum of the smallest angles (25° + 25°) is less than the largest angle (130°), the sides opposite the smaller angles would never meet to form a triangle since they would be diverging from each other instead of converging. Hence, no triangle can be constructed with these given angles.