Question

Andrea has 3 tiles.

One is a regular octagon, one is a regular pentagon and one is a regular pentagon.
Andrea thinks 3 tiles will fit together perfectly.
Show calculations to show that she is wrong.

Answer 1

Explanation:

We are going to start by working out the interior angles so first of all to work out the interior angle we used the formula: num of sides - 2 * 180 for the sum of degrees in a shape.

Lets test this formula.

Lets say we have a square it has 4 sides 4-2 = 2 *180 = 360 this is correct,meaning we can trust this formula.

Now lets put it to use.

Octagon has 8 sides - 2 = 6.

6 * 180 = 1080

Pentagon has 5 sides - 2 = 3

3 * 180 = 540

Another Pentagon 5 sides - 2 = 3

3 * 180 = 540

We have to find out a single angle because it is one side that joins to the other, also if it is a perfect fit then all the single angles must add up to 360.

1080/8 sides = 135 degrees

540 / 5 sides = 108 degrees

540 / 5 sides = 108 degrees

We add these up,

135 + 108 + 108 = 351 which cannot be a possible fit because we need 360 degrees.

Hope this helps