Which Triangle??

Geometry Level 1

A triangle has angles with measures ( x + 40 ) ∘ , (x + 40)^\circ, ( 2 x + 20 ) ∘ , (2x + 20)^\circ, and ( 3 x ) ∘ . (3x)^\circ. What type of triangle is this?

Equilateral triangle Obtuse angled triangle Scalene triangle Right angled triangle

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Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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3 solutions

We know that the sum of angles of a triangle(on an Euclidean plane) is supplementary.

Hence x + 40 + 2 x + 20 + 3 x = 180 x+40 + 2x+20+3x =180

6 x + 60 = 180 6x+60=180

x + 10 = 180 6 x+10 =\frac{180}{6}

Hence x = 20 x=20

And we get that the three angles equal to 60º, therefore the triangle is an equilateral.

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x+40 + 2x+20 + 3x = 180 => 6x + 60 = 180 => 6x = 120 => x = 20 =>

1st = 60; 2nd = 60; 3rd = 60

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Fox To-ong
Jan 12, 2015

x = 20, all angles = 60

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