Question

$\square$ABCD is a trapezium in which side AB || side DC, If $\angle$A = $\angle$B = 40$°$, what are the measures of the other two angles?

Answer 1

$$\begin{gathered} \angle \mathrm{A}+\angle \mathrm{D}=180°(\mathrm{AB}\parallel \mathrm{DC}\mathrm{and}\mathrm{angles}\mathrm{on}\mathrm{the}\mathrm{same}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{transversal} \\ \mathrm{are}\mathrm{supplementary}.) \\ \mathrm{Or}, \\ \angle \mathrm{D}=180°-40° \\ =140° \\ \mathrm{Similarly}, \\ \angle \mathrm{B}+\angle \mathrm{C}=180° \\ \Rightarrow \angle \mathrm{C}=180°-40° \\ =140° \\ \mathrm{Therefore},\mathrm{the}\mathrm{other}\mathrm{two}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{trapezium}\mathrm{are}140°\mathrm{and}140°. \end{gathered}$$