If the 3 angles of a triangle are 84 (x+59) and (x+51) , find the value of x.

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.

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