Use \(a+b+c=180^\circ\). Substituting the relationships gives \((b+15)+b+(b+60)=180\).

Thus \(3b+75=180\), so \(b=35^\circ\). Then \(a=50^\circ\) and \(c=95^\circ\).

The remaining three sectors are vertically opposite these sectors, so the six angles are \(50^\circ,35^\circ,95^\circ,50^\circ,35^\circ,95^\circ\) in cyclic order.

Answer

\(a=50^\circ,\ b=35^\circ,\ c=95^\circ\); the opposite three repeat these sizes.