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Secondary 1 | Maths
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pls help with this question 9 ASAP ty
Date Posted: 3 years ago
Views: 292
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If the interior angle = 152.5°, then one exterior angle = 180° - 152.5° = 27.5°
Sum of exterior angles of any polygon = 360°
Number of exterior angles = 360° ÷ 27.5 = 13 1/11
The number of interior angles has to be a positive integer which is equal to or bigger than 3 (3,4,5,6,10,25, etc) . But we have obtained 13 1/11 from the working. So the calculation must be wrong since number of angles cannot be a mixed number.
Sum of exterior angles of any polygon = 360°
Number of exterior angles = 360° ÷ 27.5 = 13 1/11
The number of interior angles has to be a positive integer which is equal to or bigger than 3 (3,4,5,6,10,25, etc) . But we have obtained 13 1/11 from the working. So the calculation must be wrong since number of angles cannot be a mixed number.
Alternative answer:
Interior angle of a regular polygon = 180° × (n - 2)/n, where n is the number of sides/interior angles.
Billy could have already known that a closest possible value to that measurement is the interior angle of a regular 13-gon:
180° × (13 - 2)/13 = 180° × 11/13 = 152 4/13 ° or ≈ 152.31°
The next closest possible value to that measurement is the interior angle of a regular 14-gon :
180° × (14 - 2)/14 = 180° × 12/14 = 154 2/7 ° or ≈ 154.29°
Since 152.5° lies between these two values and it is not possible to have a regular polygon between 13 and 14 sides, the measurement must be wrong.
Interior angle of a regular polygon = 180° × (n - 2)/n, where n is the number of sides/interior angles.
Billy could have already known that a closest possible value to that measurement is the interior angle of a regular 13-gon:
180° × (13 - 2)/13 = 180° × 11/13 = 152 4/13 ° or ≈ 152.31°
The next closest possible value to that measurement is the interior angle of a regular 14-gon :
180° × (14 - 2)/14 = 180° × 12/14 = 154 2/7 ° or ≈ 154.29°
Since 152.5° lies between these two values and it is not possible to have a regular polygon between 13 and 14 sides, the measurement must be wrong.
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