The required angles in the transversal that cuts the parallel lines are as follows:
a = 100°
b = 80°
x = 80°
y = 80°
z = 100°
Angles form when a transversal line cuts parallel line
When two or more lines are cut by a transversal, the angles formed includes corresponding angles, alternate angles etc.
Therefore,
x + 100 = 180(angles on a straight line)
x = 180 - 100 = 80°
x ≅ y = 80° (alternate angles)
y + z = 180
z = 180 - 80 = 100°(angles on a straight line)
z ≅ a(corresponding angles)
Therefore,
a = 100°
y ≅ b(corresponding angles)
Therefore,
b = 80°
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