Respuesta :
Answer:
pentagon
Step-by-step explanation:
So at this point, we have a full rotation of 360 degrees round that point. The graph accounts for 36 degrees of that 360 degrees leaving 360-36=324 degrees left to be split between the three polygons at (Around) that point. So 324/3=108. Now we got to figure out a polygon that has all of it's angles being 108 degrees.
We can usually find that if we know the number of sides of the polygon but we don't but here is the formula 180(n-2)/n=108
Cross multiply gives
108n=180(n-2)
Distribute
108n=180n-360
subtract 180n on both sides
-72n=-360
Divide both sides by -72
giving n=5
So a 5 side polygon is a pentagon
Three identical regular polygons fitted together at one point are regular Pentagons.
Measure of the interior angle of a polygon is given by,
Interior angle of a polygon = [tex]\frac{(n-2)\times 180^\circ}{n}[/tex]
Where 'n' = number of sides of the polygon
Let the number of regular polygons fitted together at one point = x
Therefore, sum of one interior angle of all polygons at a point = [tex]\frac{x(n-2)\times 180^\circ}{n}[/tex]
It has been given in the question "36° is the gap left when 3 identical regular polygons have fitted together at a point."
Therefore, sum of interior angles of all polygons joining at a point with the gap = [tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ[/tex]
Since, sum of angles at a point is always 360°.
[tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ=360^\circ[/tex]
[tex]\frac{3(n-2)\times 180^\circ}{n}=324^\circ[/tex]
[tex]540n-1080=324n[/tex]
[tex]540n-324n=1080[/tex]
[tex]216n=1080[/tex]
[tex]n=5[/tex]
Therefore, polygons fitted at one point are Pentagons.
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