How are corresponding angles of similar figures related?

The angles of similar figures are equal. That is what gives them the same shape.
The sides of similar figures are in equal ratios.
When two shapes are similar, it means that their angles are equal and their sides are in the same ratio.
In the example below, the corresponding angles are equal, but all of the sides are in equal proportions.
Say that angle A is 30˚. Then, angle D is also 30˚. If angle B is 50˚, angle E must also be 50˚.
Angles A and D are corresponding angles and are equal.
Angles B and E are corresponding angles and are equal.
Angles C and F are corresponding angles and are equal.
The lengths of the sides are in the ratio. 1 :2
Side AB = 10, so side DE = 20.