The three angles of a triangle add to 180°.
84 +(x+59) +(x+51) = 180
2x +194 = 180 . . . . . . . . . . collect terms
x +97 = 90 . . . . . . . . . . . .. divide by 2
x = -7 . . . . . . . . . . . . . . . . . subtract 97. Yes, the result is negative.
The value of x is –7. (negative seven)
_____
Check:
The two angles involving x are (x+59) = (-7+59) = 52, and (x+51) = (-7+51) = 44. That makes the three anges of the triangle 84°, 52° and 44°. When you add these values, you get 84°+52°+44° = 180°, as you should.
