1. **State the problem:** We have a circle with a triangle inscribed. One angle inside the circle is $37^\circ$. There is a tangent line touching the circle at the vertex where the triangle meets the circle, and an angle $x$ is formed between this tangent and a side of the triangle outside the circle. We need to find $x$. 2. **Recall the tangent-secant angle theorem:** The angle formed between a tangent and a chord drawn from the point of tangency is equal to the angle in the alternate segment of the circle. This means $x$ equals the angle inside the circle opposite to the chord. 3. **Apply the theorem:** Since the angle inside the circle adjacent to the tangent is $37^\circ$, the angle $x$ formed by the tangent and the chord outside the circle is also $37^\circ$. 4. **Conclusion:** Therefore, $x = 37^\circ$.