Question

The interior angles of a hexagon are x∘,(x+1)∘,(x+2)∘,(x+3)∘,(x+4)∘, and (x+5)∘. What is x?

Answer 1

The sum of the exterior angles is 360 deg. Each interior angle is supplementary to its corresponding exterior angle, so


`(180-x)^\circ+(180-x-1)^\circ+(180-x-2)^\circ+(180-x-3)^\circ+(180-x-4)^\circ+(180-x-5)^\circ=(1065-6x)^\circ=360^\circ`

So you have


`1065-6x=360\implies 6x=705\implies x=\frac{235}2=117.5`