In the adjoining figure, the sum of the measures of the angles $$a$$, $$b$$, $$c$$, $$d$$, $$e$$, $$f$$ is

Three straight lines pass through the middle point of the figure and cut out three triangles, one carrying the angles $$a$$ and $$b$$, one carrying $$e$$ and $$f$$, and one carrying $$c$$ and $$d$$. The three angles of these triangles at the middle point are vertically opposite the three remaining angles around that point, so the three of them add up to half of $$360^\circ$$, which is $$180^\circ$$. All nine angles of the three triangles add up to $$3 \times 180^\circ = 540^\circ$$, so the six marked angles add up to $$540^\circ - 180^\circ = 360^\circ$$.