how many triangles can be constructed with angles measuring 10º, 80º, and 90º?
How many triangles can be constructed with angles measuring 10º, 80º, and 90º?
To determine the number of triangles that can be constructed with given angles, we need to consider the triangle angle sum theorem, which states that the sum of the interior angles of a triangle is always 180 degrees.
In this case, we have angles measuring 10º, 80º, and 90º. To form a triangle, the sum of these angles must be equal to 180º.
So, let’s calculate the sum: 10º + 80º + 90º = 180º.
Since the sum of the angles is exactly equal to 180º, it is possible to form a triangle with these angle measures. However, it’s worth noting that the triangle formed will be degenerate, meaning it will have zero area.
A degenerate triangle occurs when the three vertices of the triangle are collinear. In this case, when the angles are 10º, 80º, and 90º, the triangle would collapse into a straight line.
Therefore, while it is mathematically possible to construct a triangle with these angle measures, it would not be a traditional triangle in terms of its shape or area.