Question

Please help asap.

Answer 1

Answer:

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

Step-by-step 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 = $\bold{42^\circ}$