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?

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

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).