Question

Tick (✓) the correct answer:
If an angle of a parallelogram is two-thirds of its adjacent angle, the smallest angle of the parallelogram is
(a) 54°
(b) 72°
(c) 81°
(d) 108°

Answer 1

$$\begin{gathered} \left(\mathrm{b}\right)72° \\ \mathrm{Let}x°\mathrm{be}\mathrm{the}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{parallelogram}. \\ \mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{is}180°. \\ \therefore x+\left(\frac{2}{3}\times x\right)=180 \\ \Rightarrow x+\frac{2x}{3}=180 \\ \Rightarrow \left(x+\frac{2x}{3}\right)=180 \\ \Rightarrow \frac{5x}{3}=180 \\ \Rightarrow x=\left(180\times \frac{3}{5}\right) \\ \Rightarrow x=108 \\ \mathrm{Hence},\mathrm{one}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{is}108°. \\ \mathrm{Its}\mathrm{adjacent}\mathrm{angle}=\left(180-108\right)°=72° \\ \mathrm{Therefore},\mathrm{the}\mathrm{smallest}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{is}72°. \end{gathered}$$