\[ \dfrac{x^2}{25} + \dfrac{y^2}{4} = 1 \]

The figure above depicts the portion of the ellipse whose equation is given above, which lies in the first quadrant.

Find the acute angle (in degrees) that a line passing through the origin makes with the \(x\)-axis, such that the line divides the quarter-ellipse into two segments with equal areas.

Give your answer to 1 decimal place.

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