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## Interesting angle puzzle

Here is a nice little puzzle that has appeared from Ed Southall (@solvemymaths) I think it is a good little puzzle to get your brain going and one that should be usable in a secondary classroom as the maths is not particularly advanced. It would probably be a good one to get some students problem solving and I may give it to some students this week. My approach:

I looked at this and assumed it is all regular. I labelled the three important points ABC and my first instinct was to draw a line from A to C to make a triangle. I decided not to do this, however, when I noticed that If I drew it to the point I have labelled B then I could get a nice isosceles trapezium: From here it was just a case of using my knowledge of angles in quadrilaterals, other polygons, round a point etc to find the reflex angle required. First I used knowledge of regular pentagons to see that angle AEF must be 162.  Then I used my knowledge of isosceles trapeziums and the knowledge that AEFB is an isosceles trapezium to work out that BAE and ABF are both 18. Then I considered ABCD, again I know its an isosceles trapezium. I also know that ADGE is a square therefore i can work out that DCB and ABC both equal 72. This means the reflex angle reuired must be 288. I’ve been looking at it further, and I’m not sure I can see any other ways that would work. But if you spot a different way then I would love to hear it.