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Andrea has 3 tiles.
One is a regular octagon, one is a regular pentagon
and one is a regular hexagon.
Andrea thinks the 3 tiles will fit together perfectly,
as shown in the diagram.
Show calculations to prove that she is wrong.​

1Andrea has 3 tilesOne is a regular octagon one is a regular pentagonand one is a regular hexagonAndrea thinks the 3 tiles will fit together perfectlyas shown i class=

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sherlock03
Right so to find the interior angles of a shape you need to find the number of sides in a shape and minus 2
You then times this number by 180 to get the sum of interior angles for that shape
Let’s start with the octagon
It has 8 sides so you need to do 6*180 which gives you 1080
You divide this by 8 which gives you 135
This is one angle in the octagon
If you do this for all of the shapes you get 135, 108 and 120 degrees
If you add these all up you get 363 which is 3 degrees off of 360 which would be a perfect fit

 Andrea is incorrect. Given 3 tiles will not fit together perfectly.

Angles formed at a point:

  •  Sum of all angles around a point is 360°.

As shown in the picture,

If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.

Expression for the measure of the interior angle of a polygon,

Interior angle of a polygon = [tex]\frac{(n-2)\times 180^\circ}{n}[/tex]

Interior angle of a pentagon = [tex]\frac{(5-2)\times 180^\circ}{5}=108^\circ[/tex]

Interior angle of a hexagon = [tex]\frac{(6-2)\times 180^\circ}{6}=120^\circ[/tex]

Interior angle of an octagon = [tex]\frac{(8-2)\times 180^\circ}{8}=135^\circ[/tex]

To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°

Sum of all interior angles = 108° + 120° + 135°

                                          = 363°

   Therefore, given tiles will not fit together perfectly.

Learn more about the interior angles of a polygon here,

https://brainly.com/question/12871621?referrer=searchResults

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