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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

1 Answer

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Best answer

(D) A right triangle

Explanation:

Let the angles of △ABC be ∠A, ∠B and ∠C

Given that ∠A= ∠B+∠C …(eq1)

But, in any △ABC,

Using angle sum property, we have,

∠A+∠B+∠C=180o …(eq2)

From equations (eq1) and (eq2), we get

∠A+∠A=180o

⇒2∠A=180o

⇒∠A=180o/2 = 90o

⇒∠A = 90o

Hence, we get that the triangle is a right triangle

Therefore, option (D) is the correct answer.

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