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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