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(#M40010837) TCS question Keep an EYE

if there are maximum acute angles then how many convex hectagons are there

Asked In TCS Trishika (12 years ago)

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Srishti Bhargava  (12 years ago)

3. If an angle is acute, then the corresponding exterior angle is greater than 90°. Now, suppose a convex polygon has four or more acute angles. Since the polygon is convex, all the exterior angles are positive, so the sum of the exterior angles is at least the sum of the exterior angles supplementary to the four acute angles, which is strictly greater than 4*90° = 360°. However, this is impossible, since the sum of the exterior angles of a polygon must equal 360°, and so cannot be greater than it. It follows that the largest number of acute angles a convex polygon can have is 3.

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Jagat  (12 years ago)

there can be max 3 acute angles in a convex polygon which is a triangle.

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Raj  (12 years ago)

answer is 6... correct me if any1 knw the ans !!!1

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