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Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral.

A=

B=

C=

 

 Mar 9, 2018
edited by Guest  Mar 9, 2018
edited by Guest  Mar 9, 2018
edited by Guest  Mar 9, 2018
 #1
avatar+98130 
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This is known as a cyclic quadrilateral.....its opposite angle sum to 180°

 

So.....angle A  + angle C  = 180  ......so we have

 

(3x + 53)  + (2x - 68)   = 180   simplify

 

5x  - 15  =  180      add 15 to both sides

 

5x  =  195      divide both sides by 5

 

x  = 39

 

So   A  =   3(39) - 15 =  102°

D  =   2(39) + 30   =  108°....and B  is supplemental to this  = 180- 108 =  72°

And C   =  2(39) - 68   =  10°

 

 

cool cool cool

 Mar 9, 2018

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