Question

How to calculate the interior angle of octagon and duodecagon.

please give a common formula for it.☺

Answer 1

$\huge !!! \\ \\ \Large \sf we \: know \: that \: the \: sum \: of \: \\ \Large \sf interior \: angle \: of \: a \: regular \\ \Large \sf octagon \: is = 1080 \degree \\ \\ \large \sf \therefore measure \: of \: each \: interior \\ \\ \large \sf angle = \frac{1080 \degree}{8} \: (as \: we \: know \: \\ \large \sf that \: a \: regular \: octagon \: has \: 8 \\ \large \sf equal \: angles.) \\ \\ \large \sf = 135 \degree \:$

$\large \sf similarly \: for \: duodecagon : - \\ \\ \large \sf a \: regular \: duodecagon \: has \: \\ \large \sf 20 \: equal \: sides \: and \: angles \: \\ \large \sf with \: the \: sum \: of \: interior \\ \large \sf \: angle = 1800 \degree \\ \\ \large \sf therefore \: measure \: of \: each \\ \large \sf internal \: angle = \frac{1800 \degree}{20} \\ \large \sf = 150 \degree \\ \\ \huge !!!$