question_answer 1)

Find the values of the angles \[x,\,y\] and \[z\] in each of the following:     (i)                                  (ii)                  

Answer:

                (i) \[x={{55}^{o}}\]                 \[x+y={{180}^{o}}\] \[\Rightarrow \]               \[{{55}^{o}}+y={{180}^{o}}\] \[\Rightarrow \]               \[y={{180}^{o}}-{{55}^{o}}\] \[\Rightarrow \]               \[{{125}^{o}}\]                 \[z=y={{125}^{o}}\]                 (ii) \[{{40}^{o}}+x+{{25}^{o}}={{180}^{o}}\] \[\Rightarrow \]               \[x+65={{180}^{o}}\] \[\Rightarrow \]               \[x={{180}^{o}}-{{65}^{o}}\] \[\Rightarrow \]               \[x={{115}^{o}}\]                 \[y={{180}^{o}}-{{40}^{o}}\]                 \[={{140}^{o}}\]                 \[z+y={{180}^{o}}\] \[\Rightarrow \]               \[z+{{140}^{o}}={{180}^{o}}\] \[\Rightarrow \]               \[z={{180}^{o}}-{{140}^{o}}\]                 \[={{40}^{o}}\]