what polygon has exactly three side of equal lenghth and exactly two angles of equal measure?

you could draw an irregular pentagon like that.

a pentagon

The polygon you are describing is called an isosceles triangle. An isosceles triangle has two sides of equal length and two angles of equal measure.

To determine the type of a polygon based on its sides and angles, you can follow these steps:

1. Count the number of sides: In this case, the polygon has three sides.
2. Check if all sides have equal length: If exactly three sides have equal lengths, then you have an isosceles triangle.
3. Count the number of angles: A triangle always has three angles.
4. Check if any two angles have equal measure: If exactly two angles have the same measure while the other angle is different, it is an isosceles triangle.
5. Combine the results: If both conditions are met (three sides of equal length and two angles of equal measure), then the polygon is an isosceles triangle.

Therefore, the polygon you described is an isosceles triangle.