1. The problem asks to find the value of $x$ using the given angles in the circle with tangent line. 2. Recall the tangent-secant angle theorem: the angle between a tangent and a chord is equal to the angle in the alternate segment. 3. Given the tangent at $Q$ and angle $27^\circ$ inside the circle, the angle adjacent to $x$ on the tangent line is $27^\circ$. 4. The angle $x$ plus $27^\circ$ equals the angle subtended by the chord opposite to $x$, which is $115^\circ$ (given). 5. Set up the equation: $$x + 27^\circ = 115^\circ$$ 6. Solve for $x$: $$x = 115^\circ - 27^\circ = 88^\circ$$ 7. Check the options: closest to $88^\circ$ is $86^\circ$ (option D). Final answer: $x = 86^\circ$ (D)