Let's find angle b. This angle adds to the 102 to get 180 since the two angles form a straight angle.
102+b = 180
b = 180-102
b = 78
Then we can apply the same idea to find angle c
b+c = 180
78+c = 180
c = 180-78
c = 102
A shortcut to find angle c is to recall that vertical angles are congruent. The proof of the vertical angle theorem is effectively the steps shown above.
