SOLUTION: In triangle abc ,angle a=x+20,angle b=2x-20,angle c=3/2x.show that the triangle is equilateral

Question 1068296: In triangle abc ,angle a=x+20,angle b=2x-20,angle c=3/2x.show that the triangle is equilateral
Found 2 solutions by Boreal, rothauserc:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
angles add to 180
x+20+2x-20+1.5x=180
4.5x=180=9x/2
x=180*(2/9)=40
Angles are 40+20, 80-20, and 40*1.5, and they all equal 60 degrees.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
angles a + b + c = 180 degrees (sum of the angles of any triangle)
:
x+20 + 2x-20 + 3x/2 = 180
:
3x + 3x/2 = 180
:
6x/2 + 3x/2 = 180
:
9x/2 = 180
:
9x = 360
:
x = 40
:
a = 40+20 = 60
b = 2 * 40 - 20 = 60
c = 3 * 40 / 2 = 60
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a = b = c = 60
:
triangle abc is equalateral since all three angles are equal
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