Question

I am confused please help

Answer 1

3 tiles will not fit together.

Explanation:

Measure of an Interior angle of a polygon =
`((n-2)* 180)/(n)`

Here, n = number of sides of the polygon

Therefore, measure of the interior angles of a regular hexagon,

A =
`((6-2)* 180)/(6)`

A = 120°

Similarly, interior angle of the regular pentagon,

B =
`((5-2)* 180)/(5)`

B = 108°

Now m∠A + m∠B + m∠C = 360°

m∠C = 360° - (120° + 108°)

= 132°

To fit the given three tiles perfectly, interior angle (∠D) of the third Octagonal tile should be 132°.

D =
`((8-2)* 180)/(8)`

D = 135°

m∠C ≠ m∠D

Therefore, 3 tiles will not fit together.