Mathematics
Is it possible to have a polygon whose sum of interior angles is:
(i) 870°
(ii) 2340°
(iii) 7 right angles ?
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Answer
(i) 870°
According to the properties of a polygon, if there are n sides, then the sum of its interior angles is (2n - 4) x 90°.
So,
(2n - 4) x 90° = 870°
⇒ (2n - 4) =
⇒ 2n - 4 = 9.66……..
⇒ 2n = 9.66…. + 4
⇒ 2n = 13.66….
Since 2n must be an integer, it is not possible for 2n to equal 13.666….
Hence, it is not possible to have a polygon with a sum of interior angles equal to 870°.
(ii) 2340°
According to the properties of a polygon, if there are n sides, then the sum of its interior angles is (2n - 4) x 90°.
So,
(2n - 4) x 90° = 2340°
⇒ (2n - 4) =
⇒ 2n - 4 = 26
⇒ 2n = 26 + 4
⇒ 2n = 30
⇒ n =
⇒ n = 15
Hence, it is possible to have a polygon whose sum of interior angles is 2340°.
(iii) 7 right angles
According to the properties of a polygon, if there are n sides, then the sum of its interior angles is (2n - 4) x 90°.
Given that the sum of its interior angles is 7 right angles:
7 x 90° = 630°
So,
(2n - 4) x 90° = 630°
⇒ (2n - 4) =
⇒ 2n - 4 = 7
⇒ 2n = 7 + 4
⇒ 2n = 11
Since 2n must be an integer, 2n = 11 is not possible.
Hence, it is not possible to have a polygon whose sum of interior angles is 630°.
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