Question

The measures of $\angle$K in the isosceles trapezium KLMN is 50$°$ side KL || side NM. Find the measures of the remaining angles.

Answer 1

In the following figure,

$$\begin{gathered} \mathrm{side}\mathrm{KL}\parallel \mathrm{side}\mathrm{NM} \\ \mathrm{NK}=\mathrm{ML} \\ \left(\mathrm{Since},\mathrm{the}\mathrm{trapezium}\mathrm{is}\mathrm{isosceles}\right) \\ \angle \mathrm{K}=\angle \mathrm{L}=50° \\ \mathrm{Also}, \\ \angle \mathrm{K}+\angle \mathrm{N}=180°(\mathrm{KL}\parallel \mathrm{NM}\mathrm{and}\mathrm{angles}\mathrm{on}\mathrm{the}\mathrm{same}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{transversal} \\ \mathrm{are}\mathrm{supplementary}) \\ \mathrm{or},\angle \mathrm{N}=180°-50° \\ =130° \\ \mathrm{Similarly}, \\ \angle \mathrm{M}=130° \\ \mathrm{Therefore},\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{trapezium}\mathrm{are}50°,50°,130°\mathrm{and}130°. \end{gathered}$$