 Hello and welcome to the session. In this session we discussed the following question which says if the ratio of the interior angle to the exterior angle of a regular polygon is 7 is to 2, find the number of sides of the polygon. First of all we have each interior angle of a regular polygon of n sides is equal to 2n-4 upon n right angles and also each exterior angle of a regular polygon of n sides is equal to 4 upon n right angles. This is the key idea that we use for this question. Let's proceed with the solution now. Now according to the question we have ratio of the interior angle of a regular polygon to the exterior angle of a regular polygon. This is given as 7 is to 2 also from the key idea we have interior angle of a regular polygon is to the exterior angle of a regular polygon is equal to 2n-4 upon n right angles is to 4 upon n right angles. Thus we have 2n-4 upon n right angles is to 4 upon n right angles is equal to 7 is to 2. This means we have 2n-4 upon n into 90 degrees upon 4 upon n into 90 degrees is equal to 7 upon 2. Now 90 degree cancels with 90 degree n cancels with n and we are left with 2n-4 upon 4 is equal to 7 upon 2. Now for the cross multiplying we get 2 multiplied by 2n-4 the whole is equal to 7 multiplied by 4 that is we now have 4n-8 is equal to 28. This gives us 4n is equal to 28 plus 8 that is we now have 4n is equal to 36. Now for the value of n we divide both sides by 4. Now this 4 cancels with 4 and 4 9 times is 36 therefore we get n equal to 9. Thus the number of sides of the polygon is equal to 9. So this is our final answer. This completes the session hope you understood the solution of this question.