Question

Tick (✓) the correct answer:
If one angle of a parallelogram is 24° less than twice the smallest angle then the largest angle of the parallelogram is
(a) 68°
(b) 102°
(c) 112°
(d) 176°

Answer 1

$$\begin{gathered} \left(\mathrm{c}\right)112° \\ \mathrm{Let}x°\mathrm{be}\mathrm{the}\mathrm{smallest}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{parallelogram}. \\ T\mathrm{he}\mathrm{sum}\mathrm{of}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{is}180°. \\ \therefore x+2x-24=180 \\ \Rightarrow 3x-24=180 \\ \Rightarrow 3x=180+24 \\ \Rightarrow 3x=204 \\ \Rightarrow x=\frac{204}{3} \\ \Rightarrow x=68 \\ \therefore \mathrm{Smallest}\mathrm{angle}=68° \\ L\mathrm{argest}\mathrm{angle}=\left(180-68\right)°=112° \end{gathered}$$