Question

You’re given three angle measurements of 30°, 70°, and 80°. How many triangles can you construct using these measurements?

Answer 1

There are infinitely many triangles that can be constructed. The three angles can be fixed but the side lengths can scale up or down (larger or smaller). For example, say we had a triangle with sides of 3,4,5. A similar triangle to this would be 6,8,10. The two similar triangles have the same corresponding angles (which are congruent to one another). That example shows how it's possible to make infinitely many triangles based on scaling an original triangle. 

In short, there is no limit to how many triangles you can make as long as the angles stay the same.