Question

A regular pentagon and a regular hexagon share a side, as shown in the image below.



What is the measure of x, the angle between a side of the pentagon and a side of the hexagon?

Answer 1

I found an example: . 1. A regular hexagon and a regular octagon share a side
What is the measure of x, the angle between a side of the hexagon and a side of the octagon? answer:360 - (135 + 120) = 360 - 255 = 105°.

Answer 2

sry if i didnt help

Answer 3

it helps somewhat .
this question is so friggin hard.

Answer 4

assuming that the lengths are equally matched up, and knowing that both shapes are regular (i.e., all angles/sides are of equal size), this problem becomes relatively easy with a bit of geometry.

We want to find the angle x. Angle x is an arc of a circle (more on this in a second.) We need to find out how much of angle x there is left compared to the angles in the hexagon and pentagon.

This is where the easy part comes in. All we needed was a bit of reasoning. The total amount of the angles of a hexagon is 720 degrees. Divided by 6, that is 120 for each angle.

The total amount of the angles in a pentagon is 540. Divided by 5, that is 108 per angle.

So, having a look at your drawing, we can conclude four things from what we know: there exists an angle in the pentagon that is of 108 degrees, there exists an angle in the hexagon that is 120 degrees, there exists an angle "x" that is of unknown length, and in total these angles create a full circle (angle x is the leftover arc length).

What is angle x?

There are 360 degrees in a circle.

360 - 108 - 120 = x
x = 132!

imma make a drawing in a sec

Answer 5

oh wow thank you so much : ) i actually understand it a little bit now.