Answer:
x = 1
Explanation:
You want the value of x in this geometry where secants LJ and LB intercept arcs BJ = 145x and smaller arc MK = 55° to give angle L = 45x.
External angle
The measure of angle L is half the difference of arcs BJ and MK:
L = (BJ -MK)/2
2(45x) = (145x -55)
55 = 55x . . . . . . . . . add 55 -90x
1 = x . . . . . . . . divide by 55
The value of x is 1.
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Additional comment
We can check the angle relation with x=1:
(145 -55)/2 = 90/2 = 45 . . . . . angle L
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