Lala1345
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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ParthKohli
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Do you know the sum of angles in ANY \(n\)sided polygon?

Lala1345
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n2X180 degrees

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

ParthKohli
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You are left with this mess:\[180(n 2) = 150(n  2) + 180\]

Lala1345
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Im not really understanding :\

ParthKohli
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OK, let's see how I can make you understand.

ParthKohli
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The sum of angles in ANY polygon is \(180(n 2)\) right?

Lala1345
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Right

ParthKohli
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Two angles of this particular polygon are right angles. Do you know what a right angle is?

Lala1345
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Yes

ParthKohli
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So what'd be the sum of these two right angles?

Lala1345
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A right angle measures 90 degrees

Lala1345
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180 degrees

ParthKohli
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Nice, now what'd the sum of the rest of the angles be?

Lala1345
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150 degrees

ParthKohli
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But what'd the \(\textbf{sum}\) of them be?

Lala1345
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I dont know :\ the sum is unknown :\

ParthKohli
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In terms of \(n\), what'd it be?

Lala1345
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150 (N2)

ParthKohli
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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.

ParthKohli
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Now solve for \(n\)! :)

Lala1345
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Im still not getting it :(

Lala1345
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Thanks for your help anyways :)