Question

The measures of two angles of a quadrilateral are 55$°$ each. The third angle is 150$°$. What is the measure of the fourth angle?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{the}\mathrm{fourth}\mathrm{angle}\mathrm{be}x°. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ 55°+55°+150°+x°=360°...\left[\mathrm{Angle}\mathrm{addition}\mathrm{property}\mathrm{of}\mathrm{quadrilateral}\right] \\ \Rightarrow 260°+x°=360° \\ \Rightarrow x°=360°-260° \\ \Rightarrow x°=100° \\ \mathrm{Thus},\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{the}\mathrm{fourth}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{quadrilateral}\mathrm{is}100°. \end{gathered}$$