How many triangles exist with the given angle measures? 30°, 65°, 85°

Let's see if the three given angles add to 180 degrees

30+65+85 = 95 + 85 = 180

Since the angles add to 180 degrees, this means that a triangle is possible. Not just one triangle, but infinitely many. 

Why? Because we can scale the triangles, or dilate them. Put another way, we can enlarge or shrink any triangle with these angle measures. There are infinitely many triangles of all sorts of sizes with these angles. They will all have the same shape. These triangles are similar to one another. 



Infinitely many triangles are possible.