1) In a regular polygon the difference between the interior angles of a (n-1)sided polygon & (n+1)sided polygon is 9. find n?

2) In a regular polygon the difference between the exterior angles of a (n-1)sided polygon & (n+2)sided polygon is 6. find n?

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To solve these problems, we can use the fact that the sum of the interior angles of a regular polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides of the polygon. Similarly, the sum of the exterior angles of a regular polygon is always 360 degrees.

1) Let's find the measure of the interior angles of the (n-1)-sided polygon and the (n+1)-sided polygon.

For the (n-1)-sided polygon, the sum of the interior angles is (n-3) * 180 degrees.
For the (n+1)-sided polygon, the sum of the interior angles is (n+1-2) * 180 degrees.

We are given that the difference between these two sums is 9 degrees:
(n-3) * 180 - (n-1) * 180 = 9.

Now, we can solve this equation for n:
180n - 540 - 180n + 180 = 9
-540 + 180 = 9
-360 = 9.

Since this equation has no valid solution, it means that there is no value of n that satisfies the given conditions.

2) Similarly, let's find the measure of the exterior angles of the (n-1)-sided polygon and the (n+2)-sided polygon.

For the (n-1)-sided polygon, the sum of the exterior angles is 360 degrees.
For the (n+2)-sided polygon, the sum of the exterior angles is (n+2) * 360 degrees.

We are given that the difference between these two sums is 6 degrees:
(n+2) * 360 - 360 = 6.

Now, we can solve this equation for n:
360n + 720 - 360 = 6
360n + 360 = 6
360n = -354
n = -354/360.

Since this equation gives a non-integer solution, it means that there is no value of n that satisfies the given conditions.