Question

A non-regular hexagon has a five exterior angle measures of 55, 60, 69, 57, and 57. What is the measure of the interior angle adjacent to the sixth exterior angle?

Answer 1

the 6 exterior measures = a, b, c, d, e, f. 
Their sum is 360 degrees. 
For each one, the interior angle = 180 - exterior. 

So for your problem, 
a = 55, b = 60, c = 69, d = 57, 
e = (missing one) 
f = (remaining one, not given). 

Take 55 + 60 + 69 + 57 + e, subtract from 360 to get f. 
f = 119 - e. 

Then the interior angles are: 
125, 120, 111, 123, (180 - e), and (180 - 119 + e) = (61 + e).

Answer 2

sum of exterior angles equal 360 6th exterior = 62 sum of exterior and adjacent interior equal 180 interior angle = 118