Question

The angles of a triangle are in arithmetic progression,if the smallest angle is 50 degree.Find the other two angles

Answer 1

smallest angle = 50°

let the difference be d

then other angle are 50°+d and 50°+2d

∵sum of all angles of triangle = 180°

⇒50°+(50°+d) +(50°+2d) = 180°

⇒3d = 180° - 150° = 30°

⇒d = 10°

so others angles are 50°+10° = 60° and 50°+ 20° = 70°

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Answer 2

Let a = 50
so the arithmetic progression will be on a,a+d,a+2d
so as we know that the sum of triangle is = 180 degree therefore

a+a+d+a+2d = 180°
50° + 50° +d +50° +2d = 180
150° + 3d = 180°
3d = 30°
d = 10°

therefore our arithmetic progression would be
=a,a+d,a+2d
=50°,60°,70°