Question

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! =)

Answer 1

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

Answer 2

n-2X180 degrees

Answer 3

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

Answer 4

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

Answer 5

Im not really understanding :\

Answer 6

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

Answer 7

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

Answer 8

Right

Answer 9

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

Answer 10

Yes

Answer 11

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

Answer 12

A right angle measures 90 degrees

Answer 13

180 degrees

Answer 14

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

Answer 15

150 degrees

Answer 16

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

Answer 17

I dont know :\ the sum is unknown :\

Answer 18

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

Answer 19

150 (N-2)

Answer 20

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

Answer 21

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

Answer 22

Im still not getting it :(

Answer 23

Thanks for your help anyways :-)