Octagon

 

The sum of the internal angles of an n-sided polygon is given by 180^o • (n – 2)  

 

So for an octagon (8 sides) the sum of its internal angles equals 180^o • (8 – 2)  

 

Doing the arithmetic, this sum is 1,080^o    

 

Since it is a regular octagon, all internal angles are equal, so each one is 135^o  

 

x is a supplementary angle of one of those 135^o angles, so it equals 180^o – 135^o  

 

Thus, x = 45^o  

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