Question
How many triangles can be constructed with angles measuring 10º, 80º, and 90º?
Responses
none
none
more than one
more than one
one
Responses
none
none
more than one
more than one
one
Answers
GPT-4o mini
A triangle is defined by the sum of its interior angles being exactly 180º. In this case, the angles given are 10º, 80º, and 90º.
To verify the sum:
10º + 80º + 90º = 180º
Since the angles meet the necessary condition, a triangle with these specific angles can indeed be formed. However, any triangle with these angle measures is similar to other triangles with the same angles, but the size can vary (i.e., they can be scaled to different sizes).
Thus, the answer is **more than one**, as there can be infinitely many triangles that have angles measuring 10º, 80º, and 90º, all of which are similar.
To verify the sum:
10º + 80º + 90º = 180º
Since the angles meet the necessary condition, a triangle with these specific angles can indeed be formed. However, any triangle with these angle measures is similar to other triangles with the same angles, but the size can vary (i.e., they can be scaled to different sizes).
Thus, the answer is **more than one**, as there can be infinitely many triangles that have angles measuring 10º, 80º, and 90º, all of which are similar.