Answer:
3 tiles will not fit together.
Step-by-step explanation:
Measure of an Interior angle of a polygon = [tex]\frac{(n-2)\times 180}{n}[/tex]
Here, n = number of sides of the polygon
Therefore, measure of the interior angles of a regular hexagon,
A = [tex]\frac{(6-2)\times 180}{6}[/tex]
A = 120°
Similarly, interior angle of the regular pentagon,
B = [tex]\frac{(5-2)\times 180}{5}[/tex]
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 = [tex]\frac{(8-2)\times 180}{8}[/tex]
D = 135°
m∠C ≠ m∠D
Therefore, 3 tiles will not fit together.
