7. For a triangle to be equilateral, all 3 sides must be of equal length. This implies that all corners must be equal. To find out if this is the case we have to find variable x. Never draw conclusions from the drawing.
We know that all corners of the triangle should add up to 180. So:
2x + 2x + (3x-30) = 180 => 7x = 210 => x=30
Also, 2x = 3x-30. All cornders are 60°!
So yes, this triangle is indeed equilateral. If it is equilateral, it is for sure also isosceles (for that, only two sides need to be the same).
8.A circumcenter
8.B incenter
