Question

Find the magnitude of an internal angle of a regular polygon of 20 sides. Express it in degrees and radians.​

Answer 1

Step-by-step explanation:

$\sf { \large \bold\green{GIVEN}}$

$\sf \: No. \: of \: sides \: of \: regular \: polygon \: (n) = 20$

$\sf { \large \bold\green{TO \: FIND}}$

$\sf \: inernal \: angle \: \{ \theta \}$

$\sf { \large \bold\green { \:SOLUTION }}$

$\sf \: sum \: of \: internal \: ange \: of \: polygon \: \\ \sf \: \: \: \: \: = (n - 2)180 \degree \\ \sf \: now \: \: n \: = \: 20 \\ \sf \: sum \: of \: internal \: anges \: = \: (20 - 2) \times 180 \degree \\ \sf = 18 \times 180 \\ \sf= 3240 \degree$

$\sf \: one \: interior \: angle (\theta)= \frac{3240}{20} \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (\theta)= 162 \degree$

$\sf \: convert \: \: it \: \: into \: radian \\ \: \sf Radian \: = \frac{\pi}{180} \times Degree \\ \: \: \: \: \: \: \: \: \: \: \: \sf= \frac{\pi}{180} \times 162 \\ = \frac{9\pi}{10} \\ = 2.8274$

$\green{ \boxed{\sf \: Angle \{ \theta \} \: in \: degree\: = 162 \degree}}$

$\green{ \boxed{\sf \: Angle \{ \theta \} \: in \: radian\: = \frac{9\pi}{10} \: or \: 2.8274 }}$