The ratio of an interior angle to the exterior angle of a regular polygon is 7…
2023
The ratio of an interior angle to the exterior angle of a regular polygon is 7 : 2. The number of sides of the polygon is :
- A.
7
- B.
8
- C.
9
- D.
11
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Correct answer: C
Let the interior angle be 7x and the exterior angle be 2x.
Since the interior and exterior angles are supplementary, their sum is 180°.
So, 7x + 2x = 180°
9x = 180°
x = 20°
Exterior angle = 2x = 40°
For a regular polygon, the number of sides = 360° / exterior angle
Number of sides = 360° / 40° = 9
हिन्दी उत्तर:
माना आन्तरिक कोण 7x और बाह्य कोण 2x है।
चूँकि आन्तरिक और बाह्य कोण पूरक होते हैं, इसलिए उनका योग 180° होता है।
इसलिए, 7x + 2x = 180°
9x = 180°
x = 20°
बाह्य कोण = 2x = 40°
नियमित बहुभुज के लिए, भुजाओं की संख्या = 360° / बाह्य कोण
भुजाओं की संख्या = 360° / 40° = 9