Answer:
(a) \[x+{{50}^{o}}+{{130}^{o}}+{{120}^{o}}={{360}^{o}}\] |By angle sum property of a quadrilateral \[\Rightarrow \] \[x+{{300}^{\text{o}}}={{360}^{\text{o}}}\] \[\Rightarrow \] \[x={{360}^{\text{o}}}-{{300}^{\text{o}}}\] \[\Rightarrow \] \[x={{60}^{\text{o}}}\] (b) \[x+({{180}^{\text{o}}}-{{90}^{\text{o}}})+{{60}^{\text{o}}}+{{70}^{\text{o}}}={{360}^{\text{o}}}\] |By linear pair property and angle sum property of a quadrilateral \[\Rightarrow \] \[x+{{220}^{\text{o}}}={{360}^{\text{o}}}\] \[\Rightarrow \] \[x={{360}^{\text{o}}}-{{220}^{\text{o}}}\] \[\Rightarrow \] \[x={{140}^{\text{o}}}\] (c) \[x+{{30}^{\text{o}}}+x+({{180}^{\text{o}}}-{{30}^{\text{o}}})\] \[+({{180}^{\text{o}}}-{{60}^{\text{o}}})\,=(5-2)\,\times {{180}^{\text{o}}}\] |By linear pair property and angle sum property of a pentagon \[\Rightarrow \] \[2x+{{30}^{\text{o}}}={{110}^{\text{o}}}+{{120}^{\text{o}}}={{540}^{\text{o}}}\] \[\Rightarrow \] \[2x+{{260}^{\text{o}}}={{540}^{\text{o}}}\] \[\Rightarrow \] \[2x={{540}^{o}}-{{260}^{o}}\] \[\Rightarrow \] \[2x={{280}^{o}}\] \[\Rightarrow \] \[x=\frac{{{280}^{\text{o}}}}{2}\] \[\Rightarrow \] \[x={{140}^{\text{o}}}\] (d) \[x+x+x+x+x=(5-2)\times {{180}^{\text{o}}}\] |By angle sum property of a regular pentagon \[\Rightarrow \] \[5x={{540}^{\text{o}}}\] \[\Rightarrow \] \[x=\frac{{{540}^{\text{o}}}}{5}\] \[\Rightarrow \] \[x={{108}^{\text{o}}}\]
You need to login to perform this action.
You will be redirected in
3 sec