Maths · Trigonometrical identities and trigonometrical functions
If the interior angle of a regular polygon exceeds the exterior angle by then th
If the interior angle of a regular polygon exceeds the exterior angle by \( 132^{\circ}, \) then the number of sides of the polygon is :
- A. 15
- B. 14
- C. 13
- D. 12
Step-by-step solution
Let n be the number of sides. Interior angle = (n-2)*180/n, exterior angle = 360/n. Given: (n-2)*180/n = 360/n + 132. Multiply by n: 180n - 360 = 360 + 132n => 180n - 132n = 720 => 48n = 720 => n = 15.
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