The angle through which triangle ABC is rotated after being reflected across line l and then across line m is 48 degrees.
When a triangle is reflected across a line, the acute angles of the triangle are preserved, and their measures remain unchanged. However, when a reflection is performed twice, the overall effect is equivalent to a rotation.
Given that the acute angle between lines l and m is 24 degrees, when triangle ABC is reflected across line l followed by a reflection across line m, the total rotation angle is twice the angle between the lines.
Therefore, the total angle through which triangle ABC is rotated is 2 times 24 degrees, which equals 48 degrees.
This means that after the double reflection, triangle ABC is rotated by 48 degrees. The rotation preserves the shape of the triangle, as reflections maintain the relative positions of the vertices, and the result is a congruent image of the original triangle.