Each interior angle of a polygon is 108- How many sides does it have -

Each interior angle of a polygon = 108^∘ =2n 4/n× 90^∘ = 108 ⇒2n 4/n = 108^∘/90^∘ ⇒2n 4/n = 6/5⇒ 10n 20 = 6n ⇒ 10n 6n = 20 ⇒ 4n = 20 ⇒ n = 20/4 = 5 sides ...

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Byju's Answer

Standard VIII

Mathematics

Angle Sum Property of a Polygon

Each interior...

Question

Each interior angle of a polygon is $108^{\circ}$ . How many sides does it have ?

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Solution

Each interior angle of a polygon = $108^{\circ}$ = $\frac{2 n - 4}{n} \times 90^{\circ} = 108 \Rightarrow \frac{2 n - 4}{n} = \frac{108^{\circ}}{90^{\circ}} \Rightarrow \frac{2 n - 4}{n} = \frac{6}{5} \Rightarrow 10 n - 20 = 6 n \Rightarrow 10 n - 6 n = 20 \Rightarrow 4 n = 20 \Rightarrow n = \frac{20}{4} = 5 s i d e s$

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Each interior angle of a polygon is 108∘. How many sides does it have ?

Each interior angle of a polygon = 108∘ =2n−4n×90∘=108⇒2n−4n=108∘90∘⇒2n−4n=65⇒10n−20=6n⇒10n−6n=20⇒4n=20⇒n=204=5sides

Each interior angle of a polygon is $108^{\circ}$ . How many sides does it have ?