If three angles of a triangle are (18x+6
∘
), (10x+30
∘
) and (15x+15
∘
), then the triangle is:

The sum of all interior angles in a triangle is always 180
∘
.

(18x+6)+(10x+30)+(15x+15)=180
(18+10+15)x+(6+30+15)=180
43x+51=180
43x=180−51
43x=129
x=
43
129
​
=3
Now, substitute x=3 back into the angle expressions:

First angle=18(3)+6=54+6=60
∘


Second angle=10(3)+30=30+30=60
∘


Third angle=15(3)+15=45+15=60
∘


Since all three interior angles are exactly 60
∘
, the triangle is an equilateral triangle.