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.

Answer

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Answer

\(\boxed{363^\circ}\) is not equal to \(\boxed{360^\circ}\), so the tiles will not fit together perfectly.

Steps

Step 1 ：Find the interior angles of each polygon: \(octagon = 135^\circ\), \(pentagon = 108^\circ\), \(hexagon = 120^\circ\)

Step 2 ：Calculate the sum of the angles: \(135 + 108 + 120 = 363^\circ\)

Step 3 ：\(\boxed{363^\circ}\) is not equal to \(\boxed{360^\circ}\), so the tiles will not fit together perfectly.