Sum of angle2s

Let the center of the circle be $O$ , $\angle {PQS}$ be $α$ and $\angle {PRS}$ be $β$ . $\angle {QOR}=180\degree-40\degree=140\degree$ . Using the fact that tangent to a circle is perpendicular to the radius at the point of tangency and all radii of a circle are equal in length, we can easily get $\angle {POQ}=2α$ , $\angle {POR}=2β$ and $\angle {QOR}=\angle {QOP}+\angle {POR}=2α+2β$ . Therefore $α+β=\dfrac{140\degree}{2}=\boxed {70\degree}$ .