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Polygons — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsPolygons1 Mark
MCQ
Tick the correct answer in the following? The interior angle of a regular polygon exceeds its exterior angle by $108^\circ .$ How many sides does the polygon have?
  • A
    $16$
  • B
    $14$
  • C
    $12$
  • ✓
    $10$
✓

Answer

Correct option: D.
$10$
Each exterior angle of a regular polygon $=\frac{360}{\text{n}}$
Each interior angle of a regular polygon $=180-\frac{360}{\text{n}}$
$180-\frac{360}{\text{n}}-108=\frac{360}{\text{n}}$
$\frac{720}{\text{n}}=180-108=72$
$\text{n}=\frac{720}{72}=10$

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