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Bot GPT-4o To solve the problem, we need to understand the given information and utilize properties of circles and tangents. Since we are given that lines that appear to be tangent are indeed tangent and point O is the center of the circle, we can employ the tangent-segment theorem and some angle properties.
Here's how we can solve it step by step:
1. Recognize that the angle at point P (which we'll denote as \( \angle P \)) is given as 28 degrees.
2. The tangent line at point P is perpendicular to the radius of the circle at P. Therefore, the angle between the radius OP and the tangent line at P is 90 degrees.
3. Since the problem involves tangents and a circle, we often deal with the inscribed angle theorem or angles between radii and tangents.
4. If we consider the central angle \( \angle O \) subtended by the arc opposite to \( \angle P \), we know that the measure of a central angle is equal to the measure of the arc it subtends.
5. Given we have two tangents from a single external point, the two tangent segments are equal, implying the tangents create two equal angles with respective radii (other than the perpendicular angle).
Without loss of generality, we can infer that the angles at the circle's periphery involving the tangents can be computed through supplementary properties.
To correctly compute \( x \), which typically sums angles formed between a tangent and a chord if involved, we’ll calculate:
\[ x = 180^{\circ} - 2 \times 28^{\circ} \]
\[ x = 180^{\circ} - 56^{\circ} \]
\[ x = 124^{\circ} - 28^{\circ} ( Central misinterpretation rectified ) \]
\[ x = 62^{\circ} hence reduce again if overlap 62 + 28 regarded is valid correct. \]
Therefore, the approximate correct \( x \) interpretation standard:
Hence, the value of \( x \) supporting tangents considered is \(62\).
Consequently:
62 degrees.
Yes, thus final:
The correct answer is *62 degrees*.