the angles of the quadrant are 4x , 7x , 15x , 14x . find the smallest and largest angles of quadrant

Dear Student,
As per my interpretation your query should be the angles of quadrilateral are 4x, 7x, 15x and 14x
$$\begin{gathered} \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{sum} \mathrm{of} \mathrm{angles} \mathrm{of} \mathrm{quadrilateral} \mathrm{is} 360° \\ \mathrm{So} \mathrm{we} \mathrm{have}; \\ 4\mathrm{x}+7\mathrm{x}+15\mathrm{x}+14\mathrm{x}=360° \\ \Rightarrow 40\mathrm{x}=360 \\ \Rightarrow \mathrm{x}=\frac{360}{40}=9 \\ \mathrm{So}, \mathrm{smallest} \mathrm{angle} = 4\mathrm{x}=4\times 9=36° \\ \mathrm{And} \mathrm{largest} \mathrm{angle}=15\mathrm{x}=14\times 9=135° \end{gathered}$$
Regards