Question

Two angles of a hexagon are 140 degrees and 160 degrees.If the remaining four angles are equal,find each equal angle.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{ABCDEF}\mathrm{be}\mathrm{the}\mathrm{hexagon}. \\ \mathrm{Let}\mathrm{the}\mathrm{equal}\mathrm{angles}\mathrm{be}\mathrm{x} \\ \mathrm{Two}\mathrm{of}\mathrm{the}\mathrm{angles}\mathrm{are}\angle \mathrm{A}=140°\mathrm{and}\angle \mathrm{B}=160° \\ \mathrm{Now},\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}+\angle \mathrm{E}+\angle \mathrm{F}=720° \\ \Rightarrow 140°+160°+\mathrm{x}+\mathrm{x}+\mathrm{x}+\mathrm{x}=720° \\ \Rightarrow 300+4\mathrm{x}=720° \\ \Rightarrow 4\mathrm{x}=420° \\ \Rightarrow \mathrm{x}=105° \end{gathered}$$