(ii) 
(iii) 
(iv) 
(v) 
(vi) 
Answer:
(i) \[{{115}^{o}}=\text{ }x\text{ }+{{50}^{o}}\] \[\left| \begin{align} & \text{The exterior angle of a triangle i equal to} \\ & \text{the um of it two interior oppoite angle} \\ \end{align} \right.\] \[\Rightarrow \] \[x={{115}^{o}}-{{50}^{o}}\] \[\Rightarrow \] \[x={{65}^{o}}\] (ii) \[{{100}^{o}}=x+{{70}^{o}}\] \[\left| \begin{align} & \text{The exterior angle of a triangle is equal to} \\ & \text{the sum of its two interior opposite angles} \\ \end{align} \right.\] \[\Rightarrow \] \[x={{100}^{o}}-{{70}^{o}}\] \[x={{30}^{o}}\] (iii) \[{{125}^{o}}=\text{ }x+90\]° \[\left| \begin{align} & \text{The exterior angle of a triangle is equal to} \\ & \text{the sum of its two interior opposite angles} \\ \end{align} \right.\] \[\Rightarrow \] \[x={{125}^{o}}-{{90}^{o}}\] \[\Rightarrow \] \[x={{35}^{o}}\] (iv) \[{{120}^{o}}=x+{{60}^{o}}\] \[\left| \begin{align} & \text{The exterior angle of a triangle is equal to} \\ & \text{the sum of its two interior opposite angles} \\ \end{align} \right.\] \[\Rightarrow \] \[x={{120}^{o}}-{{60}^{o}}\] \[\Rightarrow \] \[x={{60}^{o}}\] (v) \[{{80}^{o}}=x+{{30}^{o}}\] \[\left| \begin{align} & \text{The exterior angle of a triangle is equal to} \\ & \text{the sum of its two interior opposite angles} \\ \end{align} \right.\] \[\Rightarrow \] \[x={{80}^{o}}-{{30}^{o}}\] \[\Rightarrow \] \[x={{50}^{o}}\] (vi) \[{{75}^{o}}=x+{{35}^{o}}\] \[\left| \begin{align} & \text{The exterior angle of a triangle is equal to} \\ & \text{the sum of its two interior opposite angles} \\ \end{align} \right.\] \[\Rightarrow \] \[x={{75}^{o}}-{{35}^{^{o}}}\] \[\Rightarrow \] \[x={{40}^{o}}\]
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