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?

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).

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