Finding number of sides of regular polygon with different interior angles?

[Simonsky]

Having trouble with no. 4 on the attached page - it seems to me to create a polygon with alternating interior angles: 198/108/108/198.

How can the number of sides be worked out from this?



Hope you can read it clearly!

Thanks, as always, for help.

 

[Dr.Peterson]

Having trouble with no. 4 on the attached page - it seems to me to create a polygon with alternating interior angles: 198/108/108/198.

How can the number of sides be worked out from this?

View attachment 9529
.

Perhaps you are misinterpreting something. If you continue the pattern, you definitely get a regular polygon as they say, because all angles are the same.

Can you show how you got two different angles?

 

[Simonsky]

Perhaps you are misinterpreting something. If you continue the pattern, you definitely get a regular polygon as they say, because all angles are the same.

Can you show how you got two different angles?

Thanks for reply Dr. Peterson. So I maybe having a 'gestalt' problem here and perceiving the resultant shape incorrectly. This is how I saw it:




Sorry about the rough drawing-you can see that I'm seeing the angles as 108 and 108 plus 90 when the square is added. Somehow I've over complicated it?

 

[Simonsky]

108? A regular hexagon has 6 angles of 120 each...

You're right! Silly me-not sue how I did that- the issue of course, is that I'm seeing a different angle from the regular heptagon angle when the square joins so I'm seeing the shape as having different sets of interior angles: 120 ans 120+90 (using the corrected angles.

Apologies for my sloppiness (one of those days!).

 

[Simonsky]

You're right! Silly me-not sue how I did that- the issue of course, is that I'm seeing a different angle from the regular heptagon angle when the square joins so I'm seeing the shape as having different sets of interior angles: 120 ans 120+90 (using the corrected angles.

Apologies for my sloppiness (one of those days!).

Oh dear-now I said 'heptagon' when I meant hexagon!!!! Just to get it clear at last- the angles I sea, looking at the diagram are:

 

[Dr.Peterson]

Thanks for reply Dr. Peterson. So I maybe having a 'gestalt' problem here and perceiving the resultant shape incorrectly. This is how I saw it:


View attachment 9530

Sorry about the rough drawing-you can see that I'm seeing the angles as 108 and 108 plus 90 when the square is added. Somehow I've over complicated it?

You are completely misreading the problem.

The want you to continue the pattern by adding more pairs, like this, where I have added in one more copy:


The polygon they are asking about is the one formed in the middle of the resulting figure. Can you see it?

 

[Simonsky]

You are completely misreading the problem.

The want you to continue the pattern by adding more pairs, like this, where I have added in one more copy:
View attachment 9532

The polygon they are asking about is the one formed in the middle of the resulting figure. Can you see it?

Oh........I've really misinterpreted that. I thought the question had to be easier that the way I saw it -story of my life-finding something complex in something simple!! Many thanks for sorting that out for me.