Question

solve for x:

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. Let the center of the circle be \(O\). The radius drawn to the point of tangency makes a \(90^{\circ}\) angle with the tangent.

Step2: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Also, consider the triangle formed inside the circle. The angle between the radius and the non - tangent chord is related to the inscribed angle.
We know that the angle between the tangent and the chord is equal to the inscribed angle subtended by the same arc.
The angle between the tangent and the chord is \(52^{\circ}\). The angle \(x\) is an inscribed angle and the angle between the tangent and the chord subtends the same arc as the inscribed angle \(x\).
So, \(x = 52^{\circ}\)

Answer:

\(x = 52^{\circ}\)