The interior angle of a certain polygon is 84°

Question

. If each of the other angles is 147°
how many sides does the
polygon have?

Answer 1

Let n be the number of sides of the polygon.
Since the sum of the interior angles of a polygon is (n-2) * 180°, we know that (n-2) * 180° = (n-1) * 84° + 147° * (n-1).
Expanding the equation, we get 180° * n - 360° = 84° * n - 84° + 147° * n - 147°.
Combining like terms, we get 180° * n - 360° = 231° * n - 231°.
Subtracting 231° * n - 231° from both sides, we get 180° * n - 231° = -360°.
Adding 231° to both sides, we get 180° * n = 231° - 360°.
Combining like terms, we get 180° * n = -129°.
Dividing both sides by 180°, we get n = -129° / 180°.
Therefore, the polygon has -129/180 = -43/60 sides.
However, the number of sides of a polygon must be a positive whole number, so the polygon cannot have a negative or fractional number of sides.
Therefore, there is no valid solution to this problem.