Răspuns:
a) 8; b) 10; c) 12
Explicație pas cu pas:
poligon regulat:
[tex]\alpha \degree = \frac{(n - 2) \cdot 180 \degree }{n} \iff \red{ \bf n = \frac{360 \degree }{180 \degree - \alpha \degree}} \\ [/tex]
a)
[tex]n = \frac{360 \degree }{180 \degree - 135 \degree} = \frac{360 \degree }{45 \degree} = \bf 8 \\ [/tex]
b)
[tex]n = \frac{360 \degree }{180 \degree - 144 \degree} = \frac{360 \degree }{36 \degree} = \bf 10 \\ [/tex]
c)
[tex]n = \frac{360 \degree }{180 \degree - 150 \degree} = \frac{360 \degree }{30 \degree} = \bf 12 \\ [/tex]
