Question

 What is the measure of interior angles of a regular polygon with 12 sides *​

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: {\large{\textbf{\underline{\color{indigo}{『 Ԛʋᥱꜱtioᥰ:-』}}}}}$

ғɪɴᴅ ᴛʜᴇ ʀᴀᴅɪᴀɴ ᴍᴇᴀsᴜʀᴇ ᴏғ ᴛʜᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇs ᴏғ ᴀ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴ ᴏғ 12 sɪᴅᴇs.

$\: \: \: \: \: \: \: \: \: \: \: { \large{\textbf{\underline{\color{indigo}{『 Ꭺnѕwєr:- 』}}}}}$

$\sf \: We \: know \: that , \\ \sf for \: an \: n-sided \: polygon, \\ \sf \: the \: sum \: of \: all \: interior \: angles \: is  \: \\ \sf \: (n−2)×180$

$\sf \: Therefore, \: for \: a \: regular \: polygon, \\ \sf the \: measure \: of \: each \: interior \: angle \: is \: \\ \bf  \frac{n(n−2)×180°}{n}$

$\bf \green {Given \: that,} \\ \sf \: the \: regular \: polygon \: has \: 12 \: sides.$

$\sf \large \: {\therefore \: \frac{(12 - 2)180°}{12} }$

$\sf \large\implies \: \frac{10 \times 180°}{12}$

$\sf \large \implies \: (\frac{5 \times 180°}{6} ) = 150°$

$\sf\therefore  Each \: angle \: in \: radian \: = 150° \times \frac{π}{180} = \frac{5π}{6}$

$\bf \green {Hence, \: the \: radian \: measure \: of \: the \: interior }\: \\ \bf\green{angles \: of \: a \: regular \: polygon \: of \: 12 \: sides \: is}  \bf \large \red { \frac{5π}{6} }$

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