Question

I am confused please help

Answer 1

Answer:

3 tiles will not fit together.

Step-by-step explanation:

Measure of an Interior angle of a polygon = $\frac{(n-2)\times 180}{n}$

Here, n = number of sides of the polygon

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

A = $\frac{(6-2)\times 180}{6}$

A = 120°

Similarly, interior angle of the regular pentagon,

B = $\frac{(5-2)\times 180}{5}$

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 = $\frac{(8-2)\times 180}{8}$

D = 135°

m∠C ≠ m∠D

Therefore, 3 tiles will not fit together.