Question

The ratio of exterior angle to interior angle of a regular polygon is 1:4. Find the number of sides of the polygon

Answer 1

Gɪᴠᴇɴ :-

• The ratio of exterior angle to interior angle of a regular polygon is 1:4.

Tᴏ Fɪɴᴅ :-

• Find the number of sides of the polygon ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

If a Regular Polynomial with n sides , Than :-

• Each Exterior Angle = (360/n)
• Each Interior Angle = [(n - 2)180]/n

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, The Regular Polygon has n sides.

A/q,

→ (360/n) : [(n - 2)180]/n = 1 : 4

→ (360/n) / [(n - 2)180]/n = 1/4

→ (360/n) * n/[(n - 2)180] = 1/4

→ 360/(n - 2)180 = 1/4

→ 2/(n - 2) = 1/4

→ (n - 2) = 2 * 4

→ n - 2 = 8

→ n = 8 + 2

→ n = 10 (Ans.)

Hence, The Regular Polygon has 10 sides.

Answer 2

$\mathfrak{\huge{\underline{\underline{\red{Question:-}}}}}$

✒ The ratio of exterior angle to interior angle of a regular polygon is 1:4. Find the number of sides of the polygon .

$\mathcal{\huge{\underline{\underline{\green{Answer:-}}}}}$

♦ The number of sides of the polygon is 10.

$\mathbb{\huge{\underline{\underline{\blue{SOLUTION:-}}}}}$

Exterior angle =

$\dfrac{360°}{n}$

Interior angle =

$\dfrac{n - 2}{n} \times 180°$

The given ratio of exterior angle to interior angle of a regular polygon is 1:14.

∴ (360/n) : [(n - 2)180]/n = 1 : 4

=> (360/n) / [(n - 2)180]/n = 1/4

=> (360/n) * n/[(n - 2)180] = 1/4

$= > \dfrac{2}{n - 2} = \dfrac{1}{4}$

⇒ 10=n−2

⇒ 10=n

∴ n=10

∴ Number of sides of polygon is 10.

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