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  1. #1
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    help mi wif tis questions

    i duno how to do~
    Attached Thumbnails Attached Thumbnails help mi wif tis questions-15.jpg  
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  2. #2
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    Quote Originally Posted by xiaoz
    i duno how to do~
    the first one is all substitution.

    A\;=\;\frac{\left(2n-4\right)\times90}{n} so substitute 8 for n

    A\;=\;\frac{\left(2(8)-4\right)\times90}{8} and solve

    number 2 asks you to solve for n, so lets do it...

    A\;=\;\frac{\left(2n-4\right)\times90}{n} use the distributive property

    A\;=\;\frac{2n\cdot90-4\cdot90}{n} simplify

    A\;=\;\frac{180n-360}{n} multiply both sides by n

    An\;=\;180n-360subtract 180n from both sides

    An-180n\;=\;-360 subtract

    \left(A-180\right)n\;=\;-360 divide both sides by A-180

    n\;=\;\frac{-360}{A-180} simplify

    n\;=\;\frac{360}{-A+180} simplify

    n\;=\;\frac{360}{180-A} and thats what n equals. Substitute the given number for A (157.5)

    n\;=\;\frac{360}{180-157.5} and solve, this will give you the answer for a.ii
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  3. #3
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    how to do a(iii) ?
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  4. #4
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    Hello, xiaoz!

    i duno how to do~

    a) The measurement A^o of an interior angle of a regular polygon of n sides
    . . . is given by the formula: . A\;=\;\frac{(2n-4)\times 90}{n} **

    (1) Find the measure of an interior angle of a regular polygon with 8 sides.

    How about plugging in n = 8 ?



    (2) Write n in terms of A. .Hence, find the number of sides
    of the regular polygon with interior angles measuring 157.5 each.
    This requires some knowledge of Algebra I . . . too bad!

    We have: . \frac{90(2n - 4)}{n} \;= \;A

    Multiply both sides by n:\;\;90(2n - 4) \;= \;An\quad\Rightarrow\quad 180n - 360 \;= \;An

    Then: . 180n - An \;= \;360

    Factor: . (180 - A)n \;= \;360\quad\Rightarrow\quad n \:=\:\frac{360}{180 - A}

    We are told that A = 157.5

    Plug it in and determine n.



    (3) Find the regular polygon such that when the number of sides is doubled
    the measure of an interior angle is doubled.

    This is the only one that's tricky . . .

    For n sides, the angle is: . \frac{90(2n-4)}{n}\:=\:A\quad\Rightarrow\quad\frac{180n - 360}{n}\:= \:A [1]

    For 2n sides, the angle is: . \frac{90(4n-4)}{2n}\:=\:2A\quad\Rightarrow\quad \frac{360n - 360}{4n}\:=\:A [2]

    Equate [1] and [2]: . \frac{180n - 360}{n} \:= \:\frac{360n - 360}{4n}\quad\Rightarrow\quad 720n^2  - 1440n \:= \:360n^2 - 360n

    . . which simplifies to: . 360n^2 - 1080n \:=\:0

    . . which factors: . 360n(n - 3) \:= \:0

    . . and has the positive root: . x = 3


    This checks out.

    With n = 3 we have an equilateral triangle: interior angle 60^o.

    Double the number sides and we have a hexagon: interior angle 120^o.

    . . . . . . . . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    **
    This is a really stupid way of writing the formula!

    The proper form is: . A\:=\:\frac{180(n - 2)}{n}

    It can be shown that the sum of interior angles of any n-gon is: 180(n - 2)

    If all n angles are equal, each angle measures: . \frac{180(n-2)}{n} degrees.


    Someone is going to say, "What's the difference? .They're equal!"

    Well, that is certainly true.
    This means that we will have dozens of formulas to memorize . . .

    A\;=\;\frac{(n - 2) \times 180}{n} \;= \;\frac{(2n - 4) \times 90}{n}\;= \frac{(3n - 6) \times 60}{n} \;=\;\frac{(4n - 8) \times 45}{n}

    . . . = \;\frac{(5n -10) \times 36}{n} \;= \;\frac{(6n - 12) \times 30}{n} \;= \frac{(9n - 18) \times 20}{n} \;\hdots

    Catch my drift?

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  5. #5
    Grand Panjandrum
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    I have split this thread

    Xiaoz,

    I have split this thread so that your new question is in a thread
    of its own.

    It is a good idea to create a new thread when you have a new
    question, otherwise your thread may become messy and difficult to
    follow.

    RonL
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  6. #6
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    ok..
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