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Math Help - How many sides in this polygon?

  1. #1
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    How many sides in this polygon?

    The problem states: Find the number of sides in a regular polygon if the measure of an interior angle exceeds 6 times the measure of an exterior angle by 12. I wrote this formula: 180 - x = 6x + 12. In the back of the book, they say the answer is 15, but I get a different answer when I work it out. Do I have the wrong formula?
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  2. #2
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    found the answer

    Never mind, I worked it out and found out the answer is 15.
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  3. #3
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    Hello, Motherof8!

    According to your equation, x = exterior angle.
    Did you mean that?


    Find the number of sides in a regular polygon if the measure of an interior angle
    exceeds 6 times the measure of an exterior angle by 12.
    Let: x = interior angle.

    Then: 180-x = exterior angle.


    . . \underbrace{\text{Interior }}_{x}\underbrace{\text{ is }}_{=}    \underbrace{\text{ 6 times }}_{6\; \times}\underbrace{\text{ exterior }}_{(180-x)} \underbrace{\text{ plus 12}}_{ + \;12}

    We have: . x \;=\;6(180-x) + 12 \quad\Rightarrow\quad x \;=\;1080 - 6x + 12 \quad\Rightarrow\quad 7x \:=\:1092

    Hence: . x \:=\:156\quad\hdots each interior angle is 156.


    A regular polygon of n sides has an interior angle of: / 180\,\frac{n-2}{n} degrees.

    So we have: . 180\,\frac{n-2}{n} \:=\:156 \quad\Rightarrow\quad 180n - 360 \:=\:156n \quad\Rightarrow\quad 24n \:=\:260

    Therefore: . n \,=\,15\quad\hdots The polygon has 15 sides.



    Edit: You got it . . . Good for you!
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