Question 760100
Use the formula that states that the sum of the angles of an n-sided polygon is given by
(1) S = 180*(n - 2)
We know that the sum is
(2) S = 90 + 90 + (n - 2)*144 where the last expression represent the fact that the remaining non-right angles (n-2) are each 144 degrees.
Therefore setting (2) equal to (1) we get
(3) S = 90 + 90 + (n - 2)*144 = 180*(n - 2) or
(4) 180 = (n - 2)*(180 - 144) or
(5) 180 = 36*(n - 2) or
(6) n - 2 = 180/36 or
(7) n - 2 = 5 or
(8) n = 7
Answer: The polygon has seven sides.