Question
The angles of triangle are such that one is average of
other two, then the angles are:Solution
Let the angles of the triangle be aaa, bbb, and ccc such that one angle is the average of the other two: a = (b + c)/2 Since the sum of angles in a triangle is π : a + b + c = π Substitute a: (b + c/2 + b + c = π Multiply by 2: b + c + 2b + 2c = 2π ⟹ 3b+3c = 2π Let b = π/3 and c = π/3 (satisfying b + c = 2π/3), then: a = (b + c)/ 2 = π/3
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