Q. 5

Let’s write whether it is possible not that the measurement of 5 angles of a convex hexagon are 120°, 70°, 95°, 78°, 160° respectively.

Answer :

Now for a hexagon, we know it has six sides. So let us substitute n = 6 in the formula.

Sum of interior angles is given as = (2 × 6 – 4) × 90


= (12 – 4) × 90


= 8 × 90


= 720°


Let the sixth angle be x.


Now let us add all the angles.


120 + 70 + 95 + 78 + 160 + x = 720


523 + x = 720


x = 720 – 523


x = 197°.


Since the interior angle is greater than 180°, it is not possible to have a convex hexagon with these angles. The reason is that the sum of interior and exterior angles is 180°. So it is not possible to have an interior angle greater than 180°.


Tagging |||Maths||Geometrical Proofs||Geometrical Proofs


Difficulty ||| Medium


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