Question

A regular octagon and a regular nonagon share a side, as shown in the image below.


What is the measure of x, the angle between a side of the octagon and a side of the nonagon?

Answer 1

Deja vu.

Answer 2

Do you know the measure of the interior angle of a regular octagon and a regular nonagon?

Answer 3

\( \color{Black}{\Rightarrow 180(10 - 2) = 1440}\). Divide that by \(n\), which is \(10\) here.

You get 144 as the measure of an angle in a regular octagon.

Answer 4

thank you!

Answer 5

wait, but this is a combination of 2 polygons, would it be the same?

Answer 6

\(180(6 - 2) = 180 \times 4 = 720\). Divide by 6 --> 120.

Answer 7

Now to calculate the exterior angles. The question is not done yet.

Answer 8

\( \color{Black}{\Rightarrow (180 - 120) + (180 - 144)}\)

If you actually look at that diagram, you notice that it is the addition of two exterior angles. :)

Answer 9

so 60+36?

Answer 10

no..
@ParthKohli pls check the polygon sides. they are octa & nona !!

Answer 11

I am sorry. Oops.

Answer 12

Octa = 8 sides.
Nona = 9 sides

Answer 13

Its okay

Answer 14

But you get the point

Answer 15

Ya, find the internal angles, then add them

Answer 16

I got 85

Answer 17

Hmm. Not the interior angles, but the exterior.

Answer 18

right, but if you add the interior angle, one from each polygon, will you get the extrerior?

Answer 19

Let me do my work.

\( \color{Black}{\Rightarrow 180(8 - 2) = 1440 \Longrightarrow 144^{\circ}}\)
\( \color{Black}{\Rightarrow 180(7) = 1260 \Longrightarrow 140}\)

Answer 20

(180 - 144) + (180 - 140)
36 + 40
76

Answer 21

Thank you, I think I added wrong :P