Răspuns:
a) 80°, 60°, 100, 120°; b) 30°
Explicație pas cu pas:
a)
[tex]\widehat {AB} + \widehat {BC} + \widehat {CD} + \widehat {AD} = 360 \degree[/tex]
[tex]0,(3) = \frac{3}{9} = \frac{1}{3} \\ [/tex]
[tex]0,1(6) = \frac{16 - 1}{90} = \frac{15}{90} = \frac{1}{6} \\ [/tex]
[tex]0,25 = \frac{25}{100} = \frac{1}{4} \\ [/tex]
[tex]0,2 = \frac{2}{10} = \frac{1}{5} \\ [/tex]
[tex]0,25 \widehat {AB} = 0,(3) \widehat {BC} = 0,2 \widehat {CD} = 0,1(6) \widehat {AD} \iff \\ \frac{\widehat {AB}}{4} = \frac{\widehat {BC}}{3} = \frac{\widehat {CD}}{5} = \frac{\widehat {AD}}{6} = \frac{\widehat {AB} + \widehat {BC} + \widehat {CD} + \widehat {AD}}{4 + 3 + 5 + 6} = \frac{360 \degree}{18} = 20 \degree[/tex]
[tex]\frac{\widehat {AB}}{4} = 20 \degree \implies \bf \widehat {AB} = 80 \degree\\ \frac{\widehat {BC}}{3} = 20 \degree \implies \bf \widehat {BC} = 60 \degree\\ \frac{\widehat {CD}}{5} = 20 \degree \implies \bf \widehat {CD} = 100 \degree\\ \frac{\widehat {AD}}{6} = 20 \degree \implies \bf \widehat {AD} = 120 \degree[/tex]
b)
[tex]\angle AMD = \frac{\widehat {AD} - \widehat {BC}}{2} = \frac{120 \degree - 60 \degree}{2} = \frac{60 \degree}{2} = \bf 30 \degree \\ [/tex]
