There are at least 28 different pairs of angles: 66 if the first two lines are not parallel. Your question needs to be more specific as to which angles you mean.
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If the intersected lines are parallel then the angles are called equal alternate angles
Any angle that you like.
More info needed. Are the 2 lines parallel, perpendicular, or? are the angles that you are interested in on opposite sides of the intersecting line or the same side. The intersecting line is called a transversal. If the original lines are parallel, angles between the 2 lines on opposite sides of the transversal are called alternate interior angles, etc.
The third line is known as a transversal.
Here a diagram would be great and help visualize your question. My quick though is that unless the first two lines are parallel, they must intersect at some point. With this assumption (not parallel) a triangle is formed and the inner angles a, b and c would add up to 180 degrees.