Question

Sarah had 8 guests at her birthday party. She cut her round cake into 12 equal slices. 8 of the slices were eaten. What is the angle measure of the cake that was left?

Answer 1

Answer:
`120^(\circ)`

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
`\theta=(360)/(12)=30^(\circ)`

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
`4* \theta`

`\Rightarrow 4* 30^(\circ)`

`\Rightarrow 120^(\circ)`