Question

if three interior angles of a pentagon r 100 degree, 110 degree, 90 degree nd if the other two angles are equal , find the equal angles.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{ABCDE}\mathrm{be}\mathrm{the}\mathrm{pentagon}. \\ \mathrm{Let}\angle \mathrm{A}=100°;\angle \mathrm{B}=110°;\angle \mathrm{C}=90°. \\ \mathrm{Let}\angle \mathrm{D}=\angle \mathrm{E}=\mathrm{x} \\ \mathrm{Now},\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}+\angle \mathrm{E}=540°\left(\mathbf{Angle}\mathbf{}\mathbf{sum}\mathbf{}\mathbf{property}\right) \\ \Rightarrow 100°+110°+90°+\mathrm{x}+\mathrm{x}=540° \\ \Rightarrow 300°+2\mathrm{x}=540° \\ \Rightarrow 2\mathrm{x}=540°-300° \\ \Rightarrow 2\mathrm{x}=240° \\ \Rightarrow \mathrm{x}=120° \\ \mathrm{So},\angle \mathrm{D}=\angle \mathrm{E}=120° \end{gathered}$$