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.

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