Question

How do you find measure a and c

Answer 1

You can use the measure of 112 on the similar shape to find b, as they are same side exterior angles. From there, you can find both a and c, because a/b and b/c are supplementary angles. 

a = 68 degrees

c = 68 degrees

Answer 2

So you know one angle, which is 112.  The angle to the left of 112 can be found by calculating 180 - 112, because together they create a straight angle, which is always 180 degrees. 112 plus 68 equals 180, so we know the side to the left of 112 is 68 degrees.

The given angle is equal to angle b because they're corresponding angles. We now know that angle b is 112 degrees, and angle c is 68 degrees because it's the same as the other angle.

Angle a is also 68 degrees, because it can also combine with angle b to make a 180 degree angle just like angle c can.