Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Quadrilaterals1 Mark
MCQ
How many sides does a regular polygon has if each of it's interior angle is $120^\circ ?$
A
Eight
B
Seven
✓
Six
D
Five
✓
Answer
Correct option: C.
Six
Let assume polygon is regular polygon.
The measure of an interior angle, A, of a regular polygon of n sides is given by:
$\text{A}=\frac{\text{(n}-2)180^\circ} {\text{n}}$
$\Rightarrow120^\circ=\frac{\text{(n}-2)} {\text{n}}\times180^\circ.$
$\Rightarrow\frac{120^\circ\text{n}} {180^\circ}=\text{n}-2$
$\Rightarrow\frac{2} {\text{n}}=\text{n}-2$
$\Rightarrow\text{2n}=\text{3n}-6$
$\Rightarrow\text{n}=6$
$\therefore$ The regular polygon has 6 equal sides and is called a hexagon.
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