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Question
If one angle of a triangle is equal to the sum of the other two angles, the triangle is ______.
Options
obtuse
acute
right
equilateral
Solution
If one angle of a triangle is equal to the sum of the other two angles, the triangle is right.
Explanation:
Let A, B and C be the angles of the triangle. Then, one angle of a triangle is equal to the sum of the other two angles,
i.e. ∠A = ∠B + ∠C ......(i)
As we know, ∠A = ∠B + ∠C = 180° ......[Angle sum property of a triangle]
⇒ ∠A + ∠A = 180° ......[From equation (i)]
⇒ 2∠A = 180°
⇒ ∠A = `180^circ/2`
⇒ ∠A = 90°
Hence, the triangle is right-angled.
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