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Question
If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.
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Solution
Given each angle of a triangle less than the sum of the other two
`∴∠A+∠ B+∠C`
`⇒∠A+∠A<∠A+∠B+∠C`
`⇒2∠A<180^@`
[Sum of all angles of a triangle]
`⇒∠A<90^@`
Similarly` ∠ B< 90^@ and ∠C<90^@`
Hence, the triangles acute angled.
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