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Understanding Quadrilaterals — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Quadrilaterals2 Marks
Question
Find each interior angle of a regular nonagon.
✓

Answer

Exterior angle of a regular nonagon $=\frac{360^{\circ}}{9}=40^{\circ}\quad$ [in nonagon, sides are 9]
$\therefore$ Interior angle of a regular nonagon $=180^{\circ}-40^{\circ}=140^{\circ}$
Alternate Method
$\because$ Sum of all the interior angles of a nonagon
$=(n-2) \times 180^{\circ}=(9-2) \times 180^{\circ}=1260^{\circ}$
$\therefore$ Each interior angle of the nonagon $=\frac{1260^{\circ}}{9}=140^{\circ}$

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