You only get to pick two
Set two of the angles. You do not get to pick the third: it is whatever is left over from 180°, and the triangle shuts itself.
60° + 60° + 60° = 180°
All three the same: an equilateral triangle.
- Kind of triangle
- Acute
- The angle you did not pick
- 60°
Three kinds
Ready to try some? Angles-in-a-triangle worksheets
Where it usually goes wrong
All three angles get treated as free choices. They are not: once two are set the third is whatever is left of 180°, and the triangle closes itself. This is also why “a triangle with two right angles” is not a hard triangle to draw but an impossible one — the two arms never meet.
Try this
- Set both angles to 60°. The third is 60° and the triangle is equilateral, which you did not ask for and could not avoid.
- Set one to 100° and watch the room the other two have left shrink.
- Try to make two angles add to more than 180°. There is no triangle there to make.
Where this goes next
This is the fact almost every geometry problem leans on: give a diagram two angles and it has quietly given you the third.