\[\begin{align}  & \text{The total angle in a circle } \\ & \left[ {{(6x+12)}^{\circ }}+{{(5x)}^{\circ }}+{{(16x-24)}^{\circ }}+{{(5x)}^{\circ }}+{{(4x+12)}^{\circ }} \right]=360 \\ & {{(36x)}^{\circ }}={{360}^{\circ }} \\ & x=10 \\ & \text{Those offering maths in degrees will be (}5x{{)}^{\circ }}={{(5\times 10)}^{\circ }}={{50}^{\circ }} \\ & \text{The number of those offering maths will =}\frac{{{50}^{\circ }}}{{{360}^{\circ }}}\times \frac{80}{1}=\frac{100}{9}\approx 11 \\ & \text{None of the options are correct} \\ & \text{Alternative method} \\ & {{360}^{\circ }}\to 80 \\ & {{50}^{\circ }}\to x \\ & x=\frac{80\times {{50}^{\circ }}}{360}\approx 11 \\\end{align}\]