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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