Question

The sides of a regular hexagon are produced in order.prove that the sum of the exterior Angeles so formed is 4right anyles

Answer 1

If a side is produced

then, exterior angle + interior adjacent angle= 180° (Linear pair)

Also, sum of angles of a 'n' sided polygon = (2n-4)×90°

So, sum of angles of a hexagon= 2(6)-4 × 90°

⇒8×90°

⇒720°

Since the hexagon is regular each interior angle is equal.

∴ each interior angle= $(\frac{720}{6} )$°

⇒ 120°

Since all the interior angles are equal all the exterior angles will also be equal.

each exterior angle= 180°-120°

⇒60°

sum of exterior angles= 6×60° (there are 6 equal exterior angles)

⇒360°

⇒4×90°