 Hello all and welcome to the session. Today the question is the exterior angle of a regular polygon is one-third of its interior angle. Find the number of sites in the polygon. Now, before starting the solution of the question, we should know some results and the first result is each interior angle of a regular polygon of n sites is equal to 2n-4 over n right angles and the second result is each exterior angle of a regular polygon of n sites is equal to 4 by n right angles. Now, this would work as a key idea for solving out this question and now we will start with the solution. Here, another question, it is given that exterior angle of a regular polygon is one-third of its interior angle. This means exterior angle of a regular polygon is equal to 1 by 3 means 1 by 3 into interior angle of a regular polygon. Now, this implies 4 by n right angles is equal to 1 by 3 into 2n by 4 over n right angles. This implies 4 by n into 90 degrees is equal to 1 by 3 into 2n minus 4 over n into 90 degrees. Now, here this n will be cancelled with n 90 degrees will be cancelled with 90 degrees and this implies 4 is equal to 2n minus 4 over 3. Now, multiplying both the sides with 3 4 into 3 is equal to 2n minus 4 over 3 into 3. This gives 4 into 3 i.e. that is 12 is equal to here 3 into 3 will be cancelled so it is equal to 2n minus 4. This implies 2n minus 4 is equal to 12 which implies is equal to 12 plus 4 which gives 1 is equal to 16. Now, here dividing both the sides with 2 will be cancelled with 2 and 2 into 8 is 16. So, this implies n is equal to 8. Therefore, the number of sides of the regular polygon is equal to 8. So, this is the solution of the given question that is all for this session. Hope you all have enjoyed this session.