Definition

Corresponding and alternative angles are equal angles. See the figure below

                                                                       a^o         b^o

                                                                 e^o       f^o

                          c^o           d^o

                        g^o         h^o

Corresponding angles are a and c, b and d, e and g, f and h. Alternative angles are e and d, f and c.

Definition

Co-interior angles sum up to give 180^o, ex: e and f, f and d

Ex: find all the angles marked in the following figure

                                                                       a^o         60^o

                                                                 e^o       f^o

                          c^o           d^o

                        g^o         h^o

Solution: a + 60 = 180 (angles on a straight line), a = 120^o

a + b = 180^o, 120 + b = 180, b = 60^o

60 + c = 180, c = 120^o, a = c (corresponding angles)

g = 60^o

b = e (corresponding angles) but b = 60^o, then e = 60^o

c = f (corresponding angles), f = 120^o