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If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Question:

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Solution:

Given each angle of a triangle less than the sum of the other two

∴ ∠X + ∠Y + ∠Z

⇒ ∠X + ∠X < ∠X + ∠Y + ∠Z

⇒ 2∠X < 180° [Sum of all the angles of a triangle]

⇒ ∠X < 90°

Similarly ∠Y < 90° and ∠Z < 90°

Hence, the triangles are acute angled.

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