## Lala1345 2 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! =)

1. ParthKohli

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

2. Lala1345

n-2X180 degrees

3. ParthKohli

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

4. ParthKohli

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

5. Lala1345

Im not really understanding :\

6. ParthKohli

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

7. ParthKohli

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

8. Lala1345

Right

9. ParthKohli

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

10. Lala1345

Yes

11. ParthKohli

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

12. Lala1345

A right angle measures 90 degrees

13. Lala1345

180 degrees

14. ParthKohli

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

15. Lala1345

150 degrees

16. ParthKohli

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

17. Lala1345

I dont know :\ the sum is unknown :\

18. ParthKohli

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

19. Lala1345

150 (N-2)

20. ParthKohli

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

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

22. Lala1345

Im still not getting it :(

23. Lala1345

Thanks for your help anyways :-)