1. **Problem statement:** We have a square ABCD folded along diagonal AC to form a triangle, then the triangle is folded again by bringing side BC onto the longer side, resulting in triangle AXC. We need to find the measure of angle $\angle AXC$. 2. **Key properties:** In a square, all sides are equal and all angles are $90^\circ$. The diagonal divides the square into two right isosceles triangles with angles $45^\circ$, $45^\circ$, and $90^\circ$. 3. **Step 1: Folding the square along diagonal AC** - Folding along diagonal AC folds vertex B onto D or vice versa, creating triangle ABC (right isosceles). - Triangle ABC has $\angle BAC = 45^\circ$, $\angle ABC = 45^\circ$, and $\angle ACB = 90^\circ$. 4. **Step 2: Folding triangle ABC by bringing side BC onto the longer side** - Side BC is folded onto side AB, creating point X on AB such that BC coincides with BX. - Since BC = AB (both sides of the square), folding BC onto AB means $BX = BC = AB$. 5. **Step 3: Analyze triangle AXC** - Points A and C are fixed. Point X lies on AB such that $BX = BC$. - Since $AB = BC$, and $BX = BC$, then $BX = AB$, so $X$ coincides with point B. But folding creates a new point X on AB, so $X$ is the reflection of C over AB. 6. **Step 4: Calculate angle $\angle AXC$** - Because of the folding, $\angle AXC$ is twice the angle between AC and AB, which is $45^\circ$. - Therefore, $\angle AXC = 2 \times 45^\circ = 90^\circ$. 7. **Step 5: Reconsider folding effect** - The problem states the folding results in a triangle AXC with angle $\angle AXC$ to be found among given options. - The folding of BC onto AB creates an angle larger than $90^\circ$. - Using geometric reflection and folding properties, the angle $\angle AXC$ equals $112.5^\circ$. **Final answer:** $\boxed{112.5^\circ}$ (Option B)