To find the value of x, take into account that the sum of the interior angles of a triangle is 180 degrees.
You havr one angle with 62 degrees, an another angle with the expression 5x-14, the expression for the other angle is obtained by subtracting the the expression 9x +16 to 180:
180 - (9x + 16) = 180 - 9x - 16 = 164 - 9x
Then, the sum of all angles is:
62 + (5x - 14) + (164 - 9x) = 180 eliminate parenthesis
62 + 5x -14 + 164 - 9x = 180 order like terms