Maddy's Cake Conundrum: Understanding Central Angles

Maddy divided her circular cake into 10 equal slices and ate 3 slices. What is the degree measure of the central angle of her slices?

• A. 108 degrees
• B. 72 degrees
• C. 90 degrees
• D. 120 degrees

Answer: (A)

To determine the degree measure of the central angle of each slice of Maddy's circular cake, first, recognize that a full circle measures 360 degrees. Since Maddy divided her cake into 10 equal slices, each slice represents a fraction of the total circle. To find the angle corresponding to each slice, divide the total degrees in a circle by the number of slices. This calculation will provide the measure of the central angle for one slice: 360 degrees ÷ 10 slices = 36 degrees per slice. Although the answer provided indicates 108 degrees, it seems there might have been a misunderstanding. The measure of 108 degrees itself does not correspond to any slice in this scenario. The calculation indicates that each slice, regardless of how many slices she ate, retains the same central angle of 36 degrees. In this case, the degree measure of a single slice is not simply about the number of slices eaten, but about how the slices are proportioned. Thus, while the provided answer does not match the calculated central angle for one slice, the correct measure for each slice remains at 36 degrees based on the division of the total circle.

Maddy had a circular cake, perfect for a celebration or just a cozy get-together. She cheerfully sliced it into 10 equal pieces and savored 3 of those delectable slices. But here’s the kicker: what’s the degree measure of the central angle of those slices? You might think this sounds like a piece of cake—pun intended!—but let’s delve into the math.

To figure out the central angle of each slice, we start with the fact that a full circle carries a hefty 360 degrees. Now, since Maddy divided her cake into 10 equal slices, she effectively chopped the circle into pieces. Every slice represents a fraction of the total circle, and we can find that central angle by dividing 360 degrees by the number of slices, which is 10. It’s like a tasty little angle breakdown!

So, 360 degrees divided by 10 slices gives us 36 degrees per slice. That's the angle for each delightful portion. Yet, if you take a closer look at Maddy's cake distribution—blessing our taste buds—there seems to be a hiccup with a suggested answer of 108 degrees. Let’s untangle this!

You see, a common pitfall in math is jumping to conclusions without verifying the calculations. Even though Maddy’s enjoyment of 3 slices adds some drama to the story, it doesn’t affect the angle of the slices still left on the plate. Each slice retains that same central angle of 36 degrees, regardless of how many slices have been devoured. Isn’t it intriguing how math can be so absolute and yet so context-driven?

You might wonder why anyone should care about such angles beyond cake. Understanding central angles isn't just about baked goods; it subtly threads into real-life scenarios—think pizza slices, pie charts, or decorating round tables. By learning the basics, we can appreciate the mathematics behind everyday experiences.

So, in conclusion, while Maddy enjoyed her slices, the degree measure for each delicious portion remained constant at 36 degrees. Remembering this solid math principle is essential as you navigate through geometry. Next time you slice a cake—celebration or not—keep your angles sharp and your slices even!