What possible “non-intellectual” voiced do we refer to today?

if triangle abc is congruent to triangle def, their interior angles are congruent, because congruent parts of congruent triangles are congruent (cpctc).

that means ∠d is congruent to ∠a; ∠d is equal to 8x - 2.

interior angles of all triangles add to equal 180 degrees, so you can set the sum of these interior angle values equal to 180 and solve for x.

180 = (8x - 2) + 22 + 72

180 = 8x - 2 + 22 + 72

180 = 8x + 92

88 = 8x

11 = x

x = 11