sqrt(29) *cos(x +68.2deg) = 3.1

So,

cos(x +68.2deg) = 3.1 / sqrt(29)

cos(x +68.2deg) = 0.57566

It is a positive cosine value, so angle (x +68.2) is in the 1st and 4th quadrants.

(x +68.2deg) = arccos(0.57566) = 54.9 deg

In the 1st quadrant:

(x +68.2deg) = 54.9 deg

x = 54.9 -68.2 = -13.3 deg

That is in the 4th quadrant. If measuring by the usual counterclockwise way,

x = 360 -13.3 = 346.7 degrees ------**

In the 4th quadrant:

(x +68.2deg) = (360 -54.9) deg

x +68.2 = 305.1 deg

x = 305.1 -68.2 = 236.9 deg ------------**

Therefore, x = 236.9 deg and 346.7 deg. --------answer.