1. We are given a triangle ABC with vertex C at the top and an isosceles triangle where sides AC and BC are equal. 2. The measure of angle m(AB) is given as $\frac{1}{4}$ of the length AC. This is a bit unclear since angle measure is usually in degrees or radians, but here it states a fraction of a segment length. 3. Assuming you want to express the length AB in terms of AC, and considering m(AB) represents the length of segment AB, then $AB = \frac{1}{4} AC$. 4. Since triangle ABC is isosceles with $AC = BC$, and if $AB = \frac{1}{4} AC$, then AB is much smaller than the equal sides AC and BC. 5. If you want to find angle measures or further relationships, you can use the Law of Cosines or other geometric properties, but no further numeric values or angles are provided. Final answer: The length of segment AB is $\frac{1}{4}$ the length of segment AC if $m(AB)$ represents length.