Question

In the given figure, two identical regular hexagons are placed side by side as shown.

Can another identical hexagon be placed to fill the angle 'z' without leaving any gap?

• A. Yes
• B. NO
• C. Can't say
• D. Data insufficient.

Answer 1

Answer: (A)

Yes

In given figure two regular hexagons are placed side by side

We know that internal angle of hexagon=$\frac{n-2}{6}\times 180={120}^0$

$\angle x={120}^0$$y={120}^0$

$\therefore \angle x+\angle y+\angle z={360}^0$

$\Rightarrow 120+120+z=360\Rightarrow z=360-240={120}^0$

$\angle z={120}^o$

Then another hexagon whose side and angle are equal to both hexagon can also fill the '$z$' angle without leaving any gap .

Hence, option A is correct.