If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

Question:

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
(a) an isosceles triangle
(b) an obtuse triangle
(c) an equilateral triangle
(d) a right triangle

Solution:

Let ∆ABC be such that ∠A = ∠B + ∠C.

In ∆ABC,

∠A + ∠B + ∠C = 180º    (Angle sum property)

⇒ ∠A + ∠A = 180º         (∠A = ∠B + ∠C)

⇒ 2∠A = 180º

⇒ ∠A = 90º

Therefore, ∆ABC is a right triangle.

Thus, if one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle.

Hence, the correct answer is option (d).

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