Question : The sum of the interior angles of a regular polygon A is 1260 degrees and each interior angle of a regular polygon B is $128 \frac{4}{7}$ degrees. The sum of the number of sides of polygons A and B is:
Option 1: 17
Option 2: 16
Option 3: 19
Option 4: 18
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Correct Answer: 16
Solution : The sum of the interior angle Polygon A = 1260° If the sides of the polygon A are n A . ⇒ (n A – 2) × 180° = 1260° ⇒ (n A – 2) = $\frac{1260°}{180°}$ = 7 ⇒ n A = (7 + 2) = 9 Each interior angle of a regular polygon B = $\frac{900}{7}$ If the sides of the polygon B are n B . ⇒ 180° × (n B – 2) = $\frac{900}{7}$ × n B ⇒ 180n B – $\frac{900}{7}$ × n B = 360 ⇒ $\frac{360}{7}$ × n B = 360 $\therefore$ n B = 7 The sum of sides of polygons A and B = 7 + 9 = 16 Hence, the correct answer is 16.
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