Find the measure of the exterior angle at vertex  c. 

The sum of exterior angles is always 360, so to solve this one, you will have to add the exterior angles all up to find x:

10x + (4x + 26) + (12x + 44) + (7x - 3) + (6x + 59) = 360

39x + 126 = 360

39x = 234

x = 6

Now, the exterior angle at vertex C is 4x + 26.

Plug in the value you got for x:

4 * (6) + 26 = 50

The answer is 50 degrees.

Remark

The exterior angles of a convex polygon add up to 360o. Therefore for this pentagon, all 5 exterior angles = 360 degrees.

Equation

4x + 26 + 12x + 44 + 7x - 3 + 6x + 59 + 10x = 360 Combine like terms.

Solve

4x + 12x + 7x + 10x + 26 + 44 - 3 + 59 = 360

39x + 126 = 360 Subtract 126 from both sides.

39x = 360 - 126

39x = 234 Divide by 39

x = 234 / 39

x = 6

Answer

C = 4x + 26

C = 4*6 + 26

C = 24 + 26

C = 50