1. **Problem statement:** We have a six-pointed star made up of 6 identical quadrilaterals. Each quadrilateral has angles marked $x$ and two angles marked $25^\circ$. We need to find the size of angle $x$. 2. **Understanding the shape:** Since the star is made of 6 identical quadrilaterals, the total angles around the center point sum to $360^\circ$. 3. **Properties of the quadrilateral:** Each quadrilateral has 4 angles, and the sum of interior angles in any quadrilateral is $360^\circ$. 4. **Angles in the quadrilateral:** From the star, each quadrilateral has two angles of $25^\circ$ and the rest are $x$. 5. **Setting up the equation:** Let the quadrilateral's angles be $x, x, 25^\circ, 25^\circ$. Then, $$2x + 2 \times 25 = 360$$ 6. **Simplify the equation:** $$2x + 50 = 360$$ 7. **Isolate $x$:** $$2x = 360 - 50$$ $$2x = 310$$ 8. **Solve for $x$:** $$x = \frac{310}{2}$$ $$x = 155$$ 9. **Answer:** The size of angle $x$ is $155^\circ$. This means each $x$ angle in the quadrilateral is $155^\circ$.