Question

an exterior angel and an interior angle of a regular are in the ratio 2 : 7 . Find the number of sides in the polygon.

→Maths ​

Answer 1

$\huge\fbox\red{Qυєsтıση}$

ᴀɴ ᴇxᴛᴇʀɪᴏʀ ᴀɴɢᴇʟ ᴀɴᴅ ᴀɴ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ʀᴇɢᴜʟᴀʀ ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 2 : 7 . ғɪɴᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ sɪᴅᴇs ɪɴ ᴛʜᴇ ᴘᴏʟʏɢᴏɴ.

$\huge\fbox\red{AɳรωεR}$

$\bf\underline{solution}$

ɢɪᴠᴇɴ : ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ : ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ = 2:7

➛ɪғ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ = 2x,ᴛʜᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ =7x

sɪɴᴄᴇ, ᴀɴ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ + ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ =180°

$\sf\implies{2x +7x = 180°}$

$\sf\implies{2x = 2 \: \times \: 20° = 40°}$

$\sf\implies{\green{\dfrac{360°}{40°}}} = 9$

Answer 2

Answer:

ɢɪᴠᴇɴ : ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ : ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ = 2:7

➛ɪғ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ = 2x,ᴛʜᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ =7x

sɪɴᴄᴇ, ᴀɴ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ + ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ =180°

\sf\implies{2x +7x = 180°}⟹2x+7x=180°

\sf\implies{2x = 2 \: \times \: 20° = 40°}⟹2x=2×20°=40°

\sf\implies{\green{\dfrac{360°}{40°}}} = 9⟹

40°

360°

=9