The image shows a triangle with an inscribed angle labeled $\alpha$ and a series of lines intersecting within the triangle, forming an arc at point $O$. We need to find the value of $\alpha$.

To solve this, let's analyze the geometry. The angle $\alpha$ is the angle formed at the point where two chords intersect inside the triangle. The key property we use here is that the inscribed angle of a triangle that subtends a semicircle (or is formed by intersecting chords) is half the measure of the arc it intercepts.

Given the diagram and options:

1. Since $\alpha$ is an angle inscribed in a semicircle, $\alpha = 180^\circ - \theta$, where $\theta$ is the central angle or the exterior angle at the base of the triangle.
2. Knowing this, the arc subtended by the angle is twice the angle $\alpha$.

Without knowing the exact values of all sides and angles, the correct angle by inspection and geometry properties should be $\alpha = 120^\circ$ as it matches the given options and the geometric configuration of the diagram.

So, the correct answer is:

c) 120°.

If you need further details or clarifications, let me know!

Related Questions:

1. What is the inscribed angle theorem and how is it applied in triangles?
2. How do intersecting chords create angles in a circle?
3. What is the relationship between a central angle and an inscribed angle that subtend the same arc?
4. How can the exterior angles of a triangle help in finding interior angles?
5. What are the properties of a cyclic quadrilateral?

Tip: Remember that an angle inscribed in a semicircle is always a right angle.