Applying the angle of intersecting secants theorem, the measure of arc JML is: 262°.
What is the Angle of Intersecting Secants Theorem?
The angle of intersecting secants theorem states that when two lines form an external angle outside a circle, the measure of the angle is half the difference between the measure of the major and minor intercepted arcs.
Thus:
m∠JKL = (measure of arc JML - measure of arc JL)/2 => angle of intersecting secants theorem
m∠JKL = 8x - 6
measure of arc JML = 25x - 13
measure of arc JL = 360 - (25x - 13)
Plug in the values
8x - 6 = [(25x - 13) - (360 - (25x - 13))/2]
Solve for x
2(8x - 6) = [(25x - 13) - (360 - 25x + 13)]
16x - 12 = [(25x - 13) - (373 - 25x)]
16x - 12 = 25x - 13 - 373 + 25x
16x - 12 = 50x - 386
16x - 50x = 12 - 386
-34x = -374
x = 11
Measure of arc JML = 25x - 13
Plug in the value of x
Measure of arc JML = 25(11) - 13 = 262°
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