Question

How many triangles can be constructed with angles measuring 80 degrees, 80 degrees and 40 degrees

Answer 1

None.

Explanation:

We have,

The measures of the three angles of a triangle are 80°, 80° and 40°.

Since, we know,

The sum of the three angles of a triangle is 180°.

So, we get,

80° + 80° + 40° = 200°, which is greater than 180°.

Thus, we cannot make any triangle using the given angle measures.

Hence, no triangle can be constructed.

Answer 2

Infinite triangles

Explanation:

A triangle can have angles which total to 180 degrees

When one triangle ABC is constructed with degrees 80, 80 and 40 respectively, then similar triangles can be formed by transforming ABC with a real scale factor say k

k can take any real values positive, negative, rational, irrational etc.

Hence we can say given a triangle ABC with given angles there can be an infinite number of triangles with the same angles which will be similarl to ABC and carry an equal proportion with corrresponding sides.