Explanation:
when a line intersects multiple parallel lines, it has the exact same intersection angles with each of the parallel lines (because each of the parallel lines has the same behavior with the intersecting lines - otherwise they would not be parallel).
and the intersection angles above and below an intersected line are the same, they are just left-right mirrored.
lastly : the sum of all angles around one point on one side of a line is always 180°, because the line can be seen as diameter of a circle, and the point as the center of the circle. and a half-circle represents 180°.
so,
1 is the mirrored intersection angle of 55°, and is therefore also 55°.
9 is the intersection angle of 55° on the parallel line, and is therefore also 55°.
7 supplements the 120° angle to be full 180°, so
7 = 180 - 120 = 60°.
10 is the intersection angle of 1 on the parallel line, and is therefore also 55°.
6 is the mirrored intersection angle of 120°, and is therefore also 120°.
8 is the mirrored intersection angle of 7, and is therefore also 60°.
5 is the intersection angle of 8 on the parallel line, and is therefore also 60°.
3 is the mirrored intersection angle of 5, and is therefore also 60°.
1 + 2 + 3 = 180°.
55° + 2 + 60° = 180°.
2 = 65°
the same for 5, 4, 55° :
5 + 4 + 55° = 180°
60° + 4 + 55° = 180°
4 = 65°