1. **State the problem:** We need to find the size of the angle marked with the letter $k$ in the triangle. 2. **Identify given angles:** The triangle has an angle of $20^\circ$ at the bottom-left vertex, an exterior angle of $120^\circ$ at the top-right vertex, and the angle $k$ at the bottom-right vertex. 3. **Use the exterior angle theorem:** The exterior angle ($120^\circ$) is equal to the sum of the two opposite interior angles. Let the interior angle at the top-right vertex be $x$. Then, $$120^\circ = 20^\circ + x$$ 4. **Solve for $x$:** $$x = 120^\circ - 20^\circ = 100^\circ$$ 5. **Sum of angles in a triangle:** The sum of interior angles in any triangle is $180^\circ$. So, $$20^\circ + 100^\circ + k = 180^\circ$$ 6. **Solve for $k$:** $$k = 180^\circ - 20^\circ - 100^\circ = 60^\circ$$ **Final answer:** The size of angle $k$ is $60^\circ$.