If the three angles of a triangle are : $$(x+15^{\circ})[\frac{6x}{5}+6^{\circ}]$$ and $$[\frac{2x}{3}+30^{\circ}]$$ then the triangle is

Sum of all angles of a triangle = 180°

=> $$(x+15^{\circ}) + (\frac{6x}{5}+6^{\circ}) + (\frac{2x}{3}+30^{\circ})$$ = 180°

=> $$15x + 18x + 10x = 129 \times 15$$

=> $$x = 3*15 = 45^{\circ}$$

Now, 1st angle = $$(x+15^{\circ})$$ = 60°

2nd angle = $$(\frac{6x}{5}+6^{\circ})$$ = 6*9+6 = 60°

3rd angle = $$(\frac{2x}{3}+30^{\circ})$$ = 30+30 = 60°

Since, all angles are equal, thus given triangle is an equilateral triangle.