The measure of 'x' is 12°, in the equation derived by the theorem 10x - 12 = 2(4x+6) option first is correct.
It is given that in circle the angle(AMC) = (10x - 12) and angle(ABC) = (4x+6).
It is required to find the measure of 'x'
What is a circle?
It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We know the angle formed by a circle chord at its center doubles the angle formed by the chord at any point on the circle's perimeter located on the same side by using this theorem, we get:
Angle(AMC) = 2×Angle(ABC)
10x - 12 = 2(4x+6)
10x - 12 = 8x + 12
10x - 8x = 12+12
2x = 24
x = 12°
Thus, the measure of 'x' is 12°, in the equation derived by the theorem 10x - 12 = 2(4x+6).
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