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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)
Solution
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.
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