Question

Three identical regular polygons fit together at one point. There is a gap of 36 °. What is the name of the polygon?

Answer 1

Answer:

Pentagon.

Step-by-step explanation:

The angle made by the 3 polygons at the point = 360 - 36

= 324 degrees.

So the interior angle of each polygon = 324/3 = 108 degrees.

So the exterior angle = 180-108 = 72 degrees and the number of side = 360 / 72 = 5.

It is a pentagon.

Answer 2

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