This question involves circle geometry, specifically angles and arcs. Let's break it down step by step.

Key Observations:

1. The given circle diagram shows:

   • An angle of $26^\circ$ subtended at the exterior by a tangent and a chord.
   • An angle $x^\circ$ subtended by the same chord but inside the circle.

2. Property Used: The angle subtended by a chord on the circle's exterior (between the tangent and chord) is equal to the angle subtended by the same chord at any point in the circle's alternate segment.

Solution:

By this circle theorem, the external angle $26^\circ$ is equal to the interior angle $x^\circ$.

Thus: $x = 26^\circ$

Final Answer:

$x = 26^\circ$

Let me know if you'd like a more detailed explanation or have additional questions.

Follow-up Questions:

1. What is the circle theorem that relates a tangent and a chord's subtended angles?
2. How can you prove this theorem geometrically?
3. What is the difference between an alternate segment angle and an inscribed angle?
4. What happens if the point where the tangent touches the circle is moved?
5. How do we use arcs and their measurements to calculate angles in such problems?

Tip:

Always look for relationships between angles subtended by the same chord, as circle theorems often link them in surprising ways!