Close
Close

Login here to access/preview our exam papers, or sign up now for your free membership!



2007
Mon
27
Aug
Miss Loi avatar

Geometry – A Pre-Pubescent Question

(13)
Tuition given in the topic of E-Maths Tuition Questions from the desk of Miss Loi at 5:02 pm (Singapore time)

Remember those Sec One days? The days when you walked into school with a stupid-looking water bottle slung across your chest and, for the boys, when the hair was just starting to grow on your legs (please don’t think sideways. tsk.).

Sadly, many students studying for their final exams tend to get so caught-up with major NC-16 topics like Transformations and Vectors that they’ve forgotten about these good o’ pre-pubescent days.

So when they see something like this in the exam,

Diagram of n-sided polygonABCDEFG is part of a regular n-sided polygon. Given that ∠CBF = ∠EFB = 45o, find n.

… they end up scrutinizing the diagram (if there’s one) for long periods, wondering if it had been drawn correctly.

Now given that a question on polygons will almost always appear somewhere in your Paper 1, Miss Loi shall help refresh your post-puberty memory by pulling this straight out from the cartoon-laden pages of your Sec One textbook:

Sum of interior angles in a n-sided polygon = (n-2)180o

Can already hear all the “Chezzzz … so simple!“.

Welcome to the egoistic world of adulthood.

頑張って!!!

Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

  1. Leave A Comment!
Comments & Reactions

13 Comments

  1. uncle sha's Avatar
    uncle sha commented in tuition class


    2007
    Aug
    28
    Tue
    8:53am
  2. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Aug
    28
    Tue
    1:31pm
     
    2

    Hey encik, you're supposed to be an ultra U-Grade joss sticks burner!

  3. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Aug
    28
    Tue
    11:40pm
     
    3

    eh is this a synergy of simultaneous equations and geometry? if i do simultaneous this way..

    let angle EBA be a

    (180 - 45 - a) divide by 360 = n
    135 - a = 360n
    135 - 360n =a (equation 1)

    [(n-2) 180] / n = 45+ a (equation 2)

    sub equation 1 into 2 and

    (180n - 360)n = 45 + 135 - 360n
    180n - 360 = 180n - 360 (n^2)
    but however after equating i get n^2 = 1
    wad de-.-""?

  4. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Aug
    28
    Tue
    11:45pm
     
    4

    actually is the equation (180 - 45 - a) / 360 = n wrong? somehow i used another polygon the numbers were wrong but if i recall it should be 180 - interior then divided by 360 = number of sides

  5. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Aug
    29
    Wed
    12:20am
     
    5

    oh nono it should be exterior angle divded by 360..got confused..

  6. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Aug
    29
    Wed
    12:27am
     
    6

    wow this is one insane q i cant solve brain isnt working..zz nvm slp time will try tmr =x

  7. 123`'s Avatar
    123` commented in tuition class


    2007
    Aug
    29
    Wed
    9:21pm
  8. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Aug
    30
    Thu
    2:17pm
     
    8

    Welcome to Jφss Sticks 123!

    Errr ... one reason for putting up this question is to show students that sometimes a diagram can be more bane than boon!

    In this case you shouldn't be scrutinizing the finer points of the diagram - you will get more confused the longer you stare at it!

    Focus on the given formula instead!

  9. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    2
    Sun
    9:53pm
     
    9

    To answer kiroii's comment on another post, the question says it's a polygon with n. How are you going to draw a such a polygon? So do you even think that the diagram above is accurate?

    BUT even though the diagram can't accurately depict an n-sided polygon, it does a fine job of depicting another polygon with a finite number of sides.

    Get the drift?

  10. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    2
    Sun
    11:02pm
     
    10

    nop i still dunget it >.< anyway miss loi uh i was wondering are you free to conduct a tution class to teach me relative velocity? in 1 lesson and what are ur rates

  11. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    2
    Sun
    11:09pm
     
    11

    Check your inbox dude. Already replied you on Thursday.

  12. 123`'s Avatar
    123` commented in tuition class


    2007
    Sep
    3
    Mon
    7:30pm
  13. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    3
    Mon
    10:00pm
     
    13

    Awww 123` Miss Loi is so touched by you putting up your workings.

    And yes n = 12 so expect to find some confetti on your head soon!

    But Miss Loi prefers to do it this way:

    As described, the diagram is highly inaccurate BUT for sure you'll see a 5-sided polygon (even though it's irregular). This will be the ONLY time Miss Loi uses the diagram.

    Now by substituting n = 5 into the formula, you'll get:

    45o + 45o + 3x = (5-2)180o

    where x is each of the unknown interior angle of the polygon.

    Solving for this you'll get x = 150o.

    Next, if each interior angle of this n-sided polygon is 150o, then the sum of all the interior angles will be 150o*n. So we can derive the final equation:

    150o*n = (n-2)180o

    If you solve this you'll get n =12 too!

    Well to each his/her own. But in this case, Miss Loi personally prefers the reliability of equations than to make potentially risky assumptions on inaccurate diagrams.

    But well done and thanks for solving this pre-pubescent question!

Post a Comment

  • * Required field
  • Your email will never, ever be published nor shared with a Nigerian banker or a pharmaceutical company.
  • Spam filter in operation.
    DO NOT re-submit if your comment doesn't appear.
  • Spammers often suffer terrible fates.
*
*

Impress Miss Loi with beautiful mathematical equations in your comment by enclosing them within alluring \LaTeX [tex][/tex] tags (syntax guide | online editor), or the older [pmath][/pmath] tags (syntax guide). Please PREVIEW your equations before posting!

CommentLuv badge
 

 

Whatsapp Instagram Twitter Facebook Close Search Login Access RSS Joss Sticks Sessions Suggested Solutions Preview O Level Additional Mathematics O Level Elementary Mathematics Secondary Three Additional Mathematics Secondary Three Elementary Mathematics Secondary Two Mathematics Secondary One Mathematics Additional Mathematics 4038 Additional Mathematics 4018 Elementary Mathematics 4017 Virus