The value of x from the given circle is 12
Circle theorem
Angle at the vertex of the circle is half the angle at its intercepted arc.
From the given circle;
The measure of <DEF = 80/2 = 4x -8
Equate both angles
4x - 8 = 80/2
Add 8 to both sides
4x - 8 + 8 = 40 + 8
4x = 48
x =12
Hence the value of x from the given circle is 12
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