Answer:[tex]120^{\circ}[/tex]
Step-by-step explanation:
Given
cake is cut into 12 equal pieces
We know the top view of cake is similar to circle .
So, if a circle is divided into 12 equal parts then
each part subtend an angle of [tex]\theta=\frac{360}{12}=30^{\circ}[/tex]
If 8 slices were eaten , then 4 slices are remaining
These 4 slices measure subtend equal angle at the center therefore
4 slice measure a total of [tex]4\times \theta [/tex]
[tex]\Rightarrow 4\times 30^{\circ}[/tex]
[tex]\Rightarrow 120^{\circ}[/tex]