(ii) 
(iii) 
(iv)
(v) 
(vi) 
Answer:
(i) \[x+{{50}^{o}}+{{60}^{o}}={{180}^{o}}\] \[\left| \text{By the angle}-\text{sum property of a triangle} \right.\] \[\Rightarrow \] \[x+{{110}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[x={{180}^{o}}-{{110}^{o}}\] \[\Rightarrow \] \[x={{70}^{o}}\] (ii) \[x+{{90}^{o}}+{{30}^{o}}={{180}^{o}}\] \[\left| \text{By the angle}-\text{sum property of a triangle} \right.\] \[\Rightarrow \] \[x+{{120}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[x={{180}^{o}}-{{120}^{o}}\] \[\Rightarrow \] \[x={{60}^{o}}\] (iii) \[x+{{30}^{o}}+{{110}^{o}}={{180}^{o}}\] \[\left| \text{By the angle}-\text{sum property of a triangle} \right.\] \[\Rightarrow \] \[x+{{140}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[x={{180}^{o}}-{{140}^{o}}\] \[\Rightarrow \] \[x={{40}^{o}}\] (iv) \[x+x+{{50}^{o}}={{180}^{o}}\] \[\left| \text{By the angle}-\text{sum property of a triangle} \right.\] \[\Rightarrow \] \[2x+{{50}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[2x={{180}^{o}}-{{50}^{o}}\] \[\Rightarrow \] \[2x={{130}^{o}}\] \[\Rightarrow \] \[x=\frac{{{130}^{o}}}{2}\] \[\Rightarrow \] \[x={{65}^{o}}\] (v) \[x+x+x={{180}^{o}}\] \[\left| \text{By the angle - sum property of a triangle} \right.\] \[\Rightarrow \] \[3x={{180}^{o}}\] \[\Rightarrow \] \[x=\frac{{{180}^{o}}}{3}\] \[\Rightarrow \] \[x={{60}^{o}}\] (vi) \[x+2x+{{90}^{o}}={{180}^{o}}\] \[\left| \text{By the angle - sum property of a triangle} \right.\] \[\Rightarrow \] \[3x+{{90}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[3x={{180}^{o}}-{{90}^{o}}\] \[\Rightarrow \] \[3x={{90}^{o}}\] \[\Rightarrow \] \[x=\frac{{{90}^{o}}}{3}\] \[\Rightarrow \] \[x={{30}^{o}}\]
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