Final answer:
The measure of angle X in triangle XYZ cannot be determined without additional information because the expressions for angles Y and Z are given in terms of a variable x that isn't defined.
Step-by-step explanation:
The measure of angle X in a triangle XYZ is sought, given the measure of angle Y is defined by the expression 6x - 5 and angle Z is defined by the expression 3x + 16. To determine the measure of angle X, we can use the fact that the sum of the interior angles in any triangle is always 180°. Therefore, we set up and solve the following equation:
6x - 5 + 3x + 16 + measure of angle X = 180°
Now, combining like terms (6x and 3x) and constants (-5 and 16), we get:
9x + 11 + measure of angle X = 180°
We are not given the value of x to simplify this further, so we cannot give a numerical value for the measure of angle X without additional information.