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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


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 27th Jan, 2024

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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