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Question -

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



Answer -

In a тИЖABC,
Let тИаA < тИаB + тИаC
┬а
тЗТтИаA + тИаA < тИаA + тИаB + тИаC
тЗТ 2тИаA < 180┬░
тЗТ тИаA < 90┬░ (тИ╡ Sum of angles of a triangle is 180┬░)
Similarly, we can prove that
тИаB < 90┬░ and тИаC < 90┬░
тИ┤ Each angle of the triangle are acute angle.

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