The numerical value of x in the expression for the interior angle of the triangle is 6.
The figure in the image is triangle.
Note that, the sum of the interior angles of a triangle add up 180 degrees.
From the figure:
Angle 1 = 66 degrees
Angle 2 = 37 degrees
Angle 3 = ( 11x + 11 ) degrees
To solve for the value of x, wee sum the interior angle of the triangle and equate 180 degrees.
Angle 1 + Angle 2 + Angle 3 = 180
Plug in the values:
66 + 37 + ( 11x + 11 ) = 180
Collect and add like terms:
66 + 37 + 11 + 11x = 180
114 + 11x = 180
11x = 180 - 114
11x = 66
x = 66/11
x = 6
Therefore, the value of x is 6.