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Lala1345

  • 3 years ago

A polygon has n sides. Two of its angles are right angles. Each of the remaining angles equal to 150 degrees. calculate n. Please help! =)

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  1. ParthKohli
    • 3 years ago
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    Do you know the sum of angles in ANY \(n\)-sided polygon?

  2. Lala1345
    • 3 years ago
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    n-2X180 degrees

  3. ParthKohli
    • 3 years ago
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    That's right. Two angles make up 180 degrees, and what is the sum of the rest of your angles?

  4. ParthKohli
    • 3 years ago
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    You are left with this mess:\[180(n -2) = 150(n - 2) + 180\]

  5. Lala1345
    • 3 years ago
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    Im not really understanding :\

  6. ParthKohli
    • 3 years ago
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    OK, let's see how I can make you understand.

  7. ParthKohli
    • 3 years ago
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    The sum of angles in ANY polygon is \(180(n -2)\) right?

  8. Lala1345
    • 3 years ago
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    Right

  9. ParthKohli
    • 3 years ago
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    Two angles of this particular polygon are right angles. Do you know what a right angle is?

  10. Lala1345
    • 3 years ago
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    Yes

  11. ParthKohli
    • 3 years ago
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    So what'd be the sum of these two right angles?

  12. Lala1345
    • 3 years ago
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    A right angle measures 90 degrees

  13. Lala1345
    • 3 years ago
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    180 degrees

  14. ParthKohli
    • 3 years ago
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    Nice, now what'd the sum of the rest of the angles be?

  15. Lala1345
    • 3 years ago
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    150 degrees

  16. ParthKohli
    • 3 years ago
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    But what'd the \(\textbf{sum}\) of them be?

  17. Lala1345
    • 3 years ago
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    I dont know :\ the sum is unknown :\

  18. ParthKohli
    • 3 years ago
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    In terms of \(n\), what'd it be?

  19. Lala1345
    • 3 years ago
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    150 (N-2)

  20. ParthKohli
    • 3 years ago
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    Yeah, so the sum of angles is \(150(n - 2) + 180\), but it also is \(180(n - 2)\). So those two are equal.

  21. ParthKohli
    • 3 years ago
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    Now solve for \(n\)! :-)

  22. Lala1345
    • 3 years ago
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    Im still not getting it :(

  23. Lala1345
    • 3 years ago
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    Thanks for your help anyways :-)

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