7. Carina baked a cake and cut it into ten equal pieces. She ate one piece and then arranged the remaining pieces evenly, as shown. What is the size of the angle at the centre of the cake between any two adjacent pieces?
A $5^{\circ}$
B $4^{\circ}$
C $3^{\circ}$
D $2^{\circ}$
E $1^{\circ}$
Solution
B

When the cake is cut into 10 equal pieces, the size of the angle at the centre of each piece is $360^{\circ} \div 10=36^{\circ}$. Therefore, when one piece is removed and the pieces rearranged, the sum of the nine equal angles created at the centre of the cake is $36^{\circ}$. Hence the size of each angle between two adjacent pieces is $36^{\circ} \div 9=4^{\circ}$.