SOLUTION: Quadrilateral ABCD is inscribed in a circle. m A is 64°, m B is (6x + 4)°, and m C is (9x - 1)°. What is m D?

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Question 938170: Quadrilateral ABCD is inscribed in a circle. m A is 64°, m B is (6x + 4)°, and m C is (9x - 1)°. What is m D?
Answer by Edwin McCravy(20059) About Me  (Show Source):
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A quadrilateral ABCD is cyclic if and only if its opposite 
angles are supplementary.

A and C are opposite angles, so they are supplementary

m∠A + m∠C = 180°
9x-1 + 64 = 180
    9x+63 = 180
       9x = 117
        x = 13°

m∠B = 6x+4 = 6(13)+4 = 82°

B and D are opposite angles, so they are supplementary

m∠B + m∠D = 180°
82° + m∠D = 180°
      m∠D = 98°
      
Edwin