The unknown angles in the parallel lines are as follows:
a.
z = 130°
y = 50°
x = 130°
b.
x = 122°
y = 128°
z = 128°
c.
p = 107.5°
How to solve angles in parallel lines?
When parallel line are cut across by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, same interior angles, same exterior angles etc.
Therefore, let's find the angles using the relationship.
a.
z = 130 degree(vertically opposite angles)
y = 180 - 130 = 50 degrees(same side interior angles)
x = 130 degrees(alternate angle to z)
b.
x = 180 - 58 = 122 degrees(same side interior angles)
y = 180 - 52 = 128 degrees(sum of angles on a straight line)
z = 128 degrees(corresponding angles to y)
c.
An isosceles triangle has two of the angles equal to each other. Therefore, the base angle of the triangle should be the same.
base angle = (180 - 35) ÷ 2
base angle = 145 / 2
base angle = 72.5 degrees
Therefore,
p = 180 - 72.5 = 107.5 degrees (sum of angles on a straight line)