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lions [1.4K]
3 years ago
8

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

Mathematics
1 answer:
Lorico [155]3 years ago
6 0
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=\dfrac{235}2=117.5
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