Answer:
x = 9
Explanation:
You want the measure of x, given inscribed angle (8x-9)° subtends an arc of measure (19x-45)°.
Inscribed angle
An inscribed angle has half the measure of the arc it subtends. This tells us the arc measure is twice the angle measure:
2(8x -9)° = (19x -45)°
16x -18 = 19x -45 . . . . . divide by °, eliminate parentheses
27 = 3x . . . . . . . . . . add 45-16x
9 = x . . . . . . . . . . . divide by 3
The value of x is 9.
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Additional comment
The inscribed angle is 63°; the arc is 126°.
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