Prove that if one angle of a triangle is equal to the sum of the other two angles, the triangle is a right angled.

In Δ ABC, let ∠ A = ∠ B + ∠ C.
But ∠ A + ∠ B + ∠ C = 180° [Sum of the angles of a triangle is 180° ]
⇒ ∠ A + ∠ A = 180°
     ⇒ 2∠ A = 180°
      ⇒ ∠ A = 90°
Hence the Δ ABC is a right angled triangle.