Question

Please help asap.

A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures $90$ degrees If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.) What is the degree measure of the fifth slice Larry eats?

Answer 1

The answer is 5th angle =
`\bold{42^\circ}`

Explanation:

Given that pizza is divided into six unequal slices.

Largest slice has an angle of
`90^\circ`.

He eats the pizza from largest to smallest.

Let the difference in angles in each slice =
`d^\circ`

1st angle =
`90^\circ`

2nd angle = 90-d

3rd angle = 90-d-d = 90 - 2d

4th angle = 90-2d-d = 90 - 3d

5th angle = 90-3d-d = 90 - 4d

6th angle = 90-4d -d = 90 - 5d

We know that the sum of all the angles will be equal to
`360^\circ` (The sum of all the angles subtended at the center).

i.e.

`90+90-d+90-2d+90-3d+90-4d+90-5d=360\\\Rightarrow 540 - 15d = 360\\\Rightarrow 15d = 540 -360\\\Rightarrow 15d = 180\\\Rightarrow d = 12^\circ`

So, the angles will be:

1st angle =
`90^\circ`

2nd angle = 90- 12 = 78

3rd angle = 78-12 = 66

4th angle = 66-12 = 54

5th angle = 54-12 = 42

6th angle = 42 -12 = 30

So, the answer is 5th angle =
`\bold{42^\circ}`