Final answer:
The value of x is found by setting up an equation using the fact that the angles formed by the perpendicular bisector YB are congruent and sum up to 180 degrees. Solving the equation (6x - 6)° + (6x - 6)° = 180° gives us x = 16.
Step-by-step explanation:
The question asks us to solve for the variable x given that YB is the perpendicular bisector of XZ and the measure of angle mYBZ is represented as (6x - 6)°. Because YB bisects XZ, we know the angles formed are congruent. If mYBZ equals (6x - 6)°, the corresponding angle on the other side of the bisector is also (6x - 6)°. Since this forms a linear pair with mYBZ, their sum should be 180° hence,
- (6x - 6)° + (6x - 6)° = 180°
- 12x - 12 = 180
- 12x = 192
- x = 16