13. If each angle of a triangle is less than the sum of the other two, prove that
the triangle is acute angled.
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Answer:
Let ∠A ∠B and ∠C be the interior angles of ΔABC
Each angle is less than the sum of the other two angles (given)
Consider ∠A < ∠B + ∠C
=> ∠A < 180° - ∠A [∠A + ∠B + ∠C = 180°]
=> 2 ∠A < 180°
=> ∠A < 90°
So ∠A is an acute angle
ΔABC is an obtuse angled triangle.
Step-by-step explanation:
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