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Quadrilateral ABCD is inscribed in a circle such that m∠A=(x2+78)∘ and m∠C=(10x+46)∘

 

What is m∠C?

RedBlue  Mar 21, 2018
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This is known as a cyclic quadrilateral......the opposite angles are suppllementary

 

So

 

x^2 + 78  + 10x + 46  = 180

 

x^2 + 10x + 124  =  180       subtract 180 from both sides

 

x^2 + 10x - 56  =  0  factor

 

(x - 4) ( x + 14)  = 0

 

Setting each factor to 0  and solving for x  produces

 

x = 4       and   x  =  -14

 

Reject the second since it produces negative angles

 

So  C  =   10(4)  + 46   =  86°

 

 

cool cool cool

CPhill  Mar 21, 2018

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