If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right angle triangle.
Question:
If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right angle triangle.
Solution:
If one angle of a triangle is equal to the sum of the other two angles
⇒ ∠B = ∠A + ∠C
In ΔABC,
Sum of all angles of a triangle is 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠B + ∠B = 180°[∠ B = ∠ A + ∠C]
⇒ 2∠B = 180°
⇒ ∠B = 180°/2
⇒ ∠B = 90°
Therefore, ABC is a right angled triangle.
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