PQRS is a cyclic quadrilateral. If $\angle P$ is three times $\angle R$ and $\angle S$ is four times $\angle Q$, then find the sum of $\angle S + \angle R$.

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**Solution:**

1. Let $\angle R = x$ and $\angle Q = y$.

2. Given:
   - $\angle P = 3x$
   - $\angle S = 4y$

3. Since PQRS is a cyclic quadrilateral, opposite angles sum to 180°:
   - $\angle P + \angle R = 180\degree \Rightarrow 3x + x = 180\degree \Rightarrow 4x = 180\degree \Rightarrow x = 45\degree$
   - $\angle Q + \angle S = 180\degree \Rightarrow y + 4y = 180\degree \Rightarrow 5y = 180\degree \Rightarrow y = 36\degree$

4. Calculate $\angle S + \angle R$:
   - $\angle S + \angle R = 4y + x = 4 \times 36\degree + 45\degree = 144\degree + 45\degree = 189\degree$

**Answer:** $189\degree$

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