1. **State the problem:** We have an isosceles triangle PQR symmetrical about axis m, with angle Q measuring 35°. We need to find the measure of angle XPR. 2. **Understand the symmetry:** Since the triangle is isosceles and symmetrical about axis m, axis m passes through vertex P and midpoint X of side QR. 3. **Properties of isosceles triangle and symmetry:** The symmetry means angles at Q and R are equal. Given angle Q = 35°, angle R = 35°. 4. **Sum of angles in a triangle:** The sum of all angles in triangle PQR is 180°. 5. **Calculate angle P:** $$\text{angle } P = 180^\circ - (35^\circ + 35^\circ) = 180^\circ - 70^\circ = 110^\circ$$ 6. **Find angle XPR:** Since X is midpoint of QR and axis m is the symmetry axis, angle XPR is half of angle P. $$\text{angle } XPR = \frac{110^\circ}{2} = 55^\circ$$ **Final answer:** $$\boxed{55^\circ}$$