Final Answer:
The measure of the acute angle of the intersecting lines is x.
Step-by-step explanation:
Composition of Two Reflections:
The composition of two reflections is equivalent to a rotation. In this case, the angle of rotation is given as 2x.
Angle of Rotation and Intersecting Lines:
When a rotation is formed by the composition of two reflections over intersecting lines, the measure of the acute angle formed by those intersecting lines is half of the angle of rotation.
Calculation:
If the angle of rotation is 2x, then the measure of the acute angle formed by the intersecting lines is (1/2) * 2x = x.
Summary:
The acute angle of the intersecting lines, in this context, is equal to x.
Therefore, the measure of the acute angle of the intersecting lines is x.