Answer:
m<QDC = 77
Step-by-step explanation:
First we need to generate an equation in order to find the value of x.
Thus:
m<QDC = ½(Arc QBC) => Inscribed Angles Theorem)
5x + 17 = ½(4x - 6 + 9x + 4)
5x + 17 = ½(13x - 2)
Multiply both sides by 2
2(5x + 17) = 13x - 2
10x + 34 = 13x - 2
Collect like terms
10x - 13x = -34 - 2
-3x = -36
Divide both sides by -3
-3x/-3 = -36/-3
x = 12
Find m<QDC:
m<QDC = 5x + 17
Plug in the value of x
m<QDC = 5(12) + 17 = 70 + 17
m<QDC = 77
