geometry

 

It's given that AE = BE  therefore triangle ABE is isoceles 

That means that angle A = angle B  therefore angles A + B = 114^o  

The total of the internal angles of a triangle is 180^o  therefore angle BEA = 66^o  

 

Since angle BEA is 66^o  then so is angle DEC because the two are vertical angles. 

So angle D + angle DEC = 31^o + 66^o = 97^o   

The total of the internal angles of a triangle is 180^o  therefore angle C = 83^o   

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