Explanation:
the handrail is a line that intersects several other lines (the stands) that are parallel to each other.
the intersection angles must be the same for each of the parallel lines. otherwise they would not be parallel, as each parallel line imitates exactly the properties of the other parallel lines.
therefore,
angle 8 = angle 6 = 130°
angle 7 = angle 5.
for angle 5 and 7 we need to consider that the sum of all angles around a point on one side of a line is 180°, because that line stands for the diameter of an imaginary circle with that point as its center.
one side of the line represents then a half-circle = 180°.
so,
180 = 130 + angle 5
angle 5 = 50° = angle 7