Question

Two angles of a quadrilateral are of measure 65° and the other two angles are equal. What is the measure of each of these two angles?

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{each}\mathrm{angle}. \\ \mathrm{Since},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{quadrilateral}\mathrm{is}360°,\mathrm{we}\mathrm{have}: \\ 65°+65°+x°+x°=360° \\ \Rightarrow 2x°+130°=360° \\ \Rightarrow 2x°=230° \\ \Rightarrow x°=115° \\ \therefore \mathrm{The}\mathrm{measure}\mathrm{of}\mathrm{each}\mathrm{angle}\mathrm{is}115°. \end{gathered}$$