Problem number 11. Carolina baked a cake and cut it into 10 equal pieces. She ate one piece and then arranged the remaining pieces evenly as shown. What is the measure of the angle between any two adjacent pieces? So first notice that originally we had 10 slices in a circle and remember that a circle is 360 degrees so that means that the angle in each slice is 360 degrees divided by 10 equals 36 degrees and if we removed one of the slices then that means we have nine slices left and the gaps between the slices must all be equal so all of the gaps between each two adjacent pieces are equal and the total amount of these gaps is equal to the angle of the removed slice because we removed that one slice that sort of missing slice has been split evenly among these nine gaps since we know the angle of one slice is 36 degrees and there are nine equal gaps then each gap has an angle of 36 degrees over nine and that is four degrees so that means that the measure of each gap is four degrees and that means the answer is b four degrees

cake slices

circle geometry

angle calculation

equal gaps

adjacent pieces