Question

Ex; 15 .....................

Answer 1

a)

$\it Unghiurile\ \widehat{AOC},\ \widehat{COB}\ sunt\ suplementare,\ deci: \\ \\ m(\widehat{AOC})+m(\widehat{COB})=180^o\ \ \ \ \ (1) \\ \\ Dar,\ m(\widehat{AOC})=4m(\widehat{COB}) \ \ \ \ \ \ \ \ (2) \\ \\ (1),\ (2) \Rightarrow 4m(\widehat{COB})+m(\widehat{COB})=180^o \Rightarrow 5m(\widehat{COB})=180^o|_{:5} \Rightarrow \\ \\ \Rightarrow\ \widehat{COB}=36^o\ \ \ \ \ (3)$

$\it (2),\ (3)\Rightarrow m(\widehat{AOC})=4\cdot36^o \Rightarrow m(\widehat{AOC})=144^o$

b)

Prelungim OC, dincolo de O, cu OD, astfel încât O∈ CD.

c)

$\it m(\widehat{AOD})=m(\widehat{COB})=36^o \ (opuse\ la\ v\^{a}rf)\\ \\ m(\widehat{BOD})=m(\widehat{AOC})=144^o \ (opuse\ la\ v\^{a}rf)$