Question

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

Answer 1

Infinite similar triangles

Explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

In a triangle the sum of its internal angles must be equal to
`180` degrees

In this problem

The sum of the internal angles is equal to
`180` degrees

so

By the sum of the internal angles, we can construct a triangle

but

By the length of the sides keeping the same internal angles, we can construct infinite similar triangles.

Answer 2

A Triangle is a polygon consisting 3 side and 3 angles. Each side can be equal to other side and also be not equal to other one but same the equal one. In terms of angle, the sum of all the 3 angles of a triangle should be 180. So with the values of angles you give, you can only construct 1 triangle because the sum of all its angle is 180.