Using the inscribed angle theorem, the value of x is: 9.
What is the Inscribed Angle Theorem?
Note that an intercepted arc is regarded as part of the circumference of a circle, which is between a chord and a tangent. Thus, based on the inscribed angle theorem, the inscribed angle measure = 1/2(the intercepted arc measure).
So, we would have:
m∠DEF = 1/2(arc DE)
m∠DEF = 4x + 19
arc DE = 360 - (28x - 2) = 360 - 28x + 2
arc DE = 362 - 28x
Plug in the values
4x + 19 = 1/2(362 - 28x)
Solve for x
2(4x + 19) = 362 - 28x
8x + 38 = 362 - 28x
8x + 28x = 362 - 38
36x = 324
x = 324/36
x = 9
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