(ii) 
(iii) 
Answer:
(i) \[y={{100}^{o}}\] | Opposite angles of a parallelogram are equal \[x+{{100}^{o}}={{180}^{o}}\] Adjacent angles in a parallelogram are supplementary \[\Rightarrow \] \[x={{180}^{o}}-{{100}^{o}}\] \[\Rightarrow \] \[x={{80}^{o}}\] \[z=x={{80}^{o}}\] (ii) \[x+{{50}^{o}}={{180}^{o}}\] |Adjacent angles in a parallelogram are supplementary \[\Rightarrow \] \[x={{180}^{o}}-{{50}^{o}}={{130}^{o}}\] \[y=x={{130}^{o}}\] |The opposite angles of a parallelogram are of equal measure \[{{180}^{o}}-z={{50}^{o}}\] \[\Rightarrow \] \[z={{180}^{o}}-{{50}^{o}}={{130}^{o}}\] (iii) \[x=90{}^\circ \] \[x+y+{{30}^{o}}=~{{180}^{o}}\] | By angle sum property of a triangle \[\Rightarrow \] \[{{90}^{o}}+y+30={{180}^{o}}\] \[\Rightarrow \] \[{{120}^{o}}+y={{180}^{o}}\] \[\Rightarrow \] \[y={{180}^{o}}-{{120}^{o}}={{60}^{o}}\] \[z+{{30}^{o}}+{{90}^{o}}={{180}^{o}}\] | By angle sum property of a triangle \[\Rightarrow \] \[z={{60}^{o}}\] (iv) \[y={{80}^{o}}\] \[x+{{80}^{o}}={{180}^{o}}\] Adjacent angles in a parallelogram are supplementary \[\Rightarrow \] \[x={{180}^{o}}-{{80}^{o}}\] \[\Rightarrow \] \[x={{100}^{o}}\] \[{{180}^{o}}-z+{{80}^{o}}={{180}^{o}}\] |Linear pair property and adjacent angles in a parallelogram are supplementary. \[\Rightarrow \] \[z={{80}^{o}}\] (v) \[={{112}^{o}}\] |Opposite angles of a parallelogram are equal \[x+y+{{40}^{o}}={{180}^{o}}\] | By angle sum property of a triangle \[\Rightarrow \] \[x+{{112}^{o}}+{{40}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[x+{{152}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[x={{180}^{o}}-{{152}^{o}}\] \[\Rightarrow \] \[x={{28}^{\text{o}}}\] \[\Rightarrow \] \[z=x={{28}^{o}}\] | Alternate angle
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