Question

Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)

Answer 1

Let the angles of triangles be a, a + d, a + 2d

We know that, sum of angles of triangle = 180°

∴ a + a + d + a + 2d = 180°

∴ 3a + 3d = 180°

∴ 3(a + d) = 180°

∴ (a + d) = `(180ϒ)/3`

∴ a + d = 60°   ......(i)

According to the given conditions,

Smallest angle, a = 5 × d

∴ a = 5d

Putting the value of an in equation (i)

∴ 5d + d = 60°

∴ 6d = 60°

∴ d = `(60ϒ)/6`  

∴ d = 10°

Putting the value of d in (i)

∴ a + d = 60°

∴ a + 10 = 60°

∴ a = 60° – 10

∴ a = 50°

∴ a + 2d = 50° + 2(10)

= 50° + 20

= 70°

∴ Angles of triangle are 50°, 60°, 70° respectively.