Answer:
x = 72°
Explanation:
You want the measure of angle x, given that it subtends arc BC of a circle in which the measures of the arcs around the circle have the ratios ...
BA : AC : CB = 3 : 3 : 4
Arc measures
Arc CB has a ratio to the sum of arcs of a circle:
CB/(BA +AC +CB) = 4/(3 +3 +4) = 4/10 = 2/5
The arcs of a circle total 360°, so ...
CB = (2/5)·360° = 144°
Inscribed angle
The angle whose measure is x is an inscribed angle with half the measure of the arc it subtends:
x = CB/2 = 144°/2
x = 72°
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Additional comment
Your labeling of the arcs as 3x, 3x, and 4x is perhaps unfortunate. The value of x in those expressions is a scale factor or multiplier that will tell you the arc measures that add up to 360°. That value of x is 36°.
The reason this is unfortunate is that there is already an x defined in the figure. It is the measure of the angle between segment BC and the tangent at B. Its value is different than the x used in the arc measure relation. If we call this value X to distinguish it from x, then we have ...
X = 4x/2 = 2x
X = 2(36)° = 72°.