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Polygons — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsPolygons1 Mark
MCQ
Tick the correct answer in the following? In a regular polygon, each interior angle is thrice the exterior angle. The number os sides of the polygon is:
  • A
    $6$
  • ✓
    $8$
  • C
    $10$
  • D
    $12$
✓

Answer

Correct option: B.
$8$
For a regular polygon with $n$ sides:
Each exterior angle $=\frac{ 360}{ \text{n}}$
Each interior angle $=180-\frac{360}{\text{n}}$
$\therefore180-\frac{360}{\text{n}}=3\Big(\frac{360}{\text{n}}\Big)$
$\Rightarrow180=4\Big(\frac{360}{\text{n}}\Big)$
$\Rightarrow\text{n}=\frac{4\times360}{180}=8$

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