Question

If the sum of the two angles of a quadrilateral is 180°. What is the sum of the remaining two angles?

Answer 1

$$\begin{gathered} \mathrm{Let}\left(x+y\right)\mathrm{be}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{remaining}\mathrm{two}\mathrm{angles}. \\ \mathrm{Since},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{quadrilateral}\mathrm{is}360°,\mathrm{we}\mathrm{have}: \\ 180°+\left(x+y\right)°=360° \\ \Rightarrow \left(x+y\right)°=180° \\ \therefore \mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{remaining}\mathrm{two}\mathrm{angles}\mathrm{is}180°. \end{gathered}$$