Question

One complementary angle is 20 degrees more than the other, find the pair of complementary angles.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{angle}=\mathrm{x} \\ \mathrm{Then}\mathrm{measure}\mathrm{of}\mathrm{its}\mathrm{complement}=90°-\mathrm{x} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ 90°-\mathrm{x}=20°+\mathrm{x} \\ \Rightarrow \mathrm{x}+\mathrm{x}=90°-20° \\ \Rightarrow 2\mathrm{x}=70° \\ \Rightarrow \mathrm{x}=\frac{70}{2}=35 \\ \mathrm{So},\mathrm{first}\mathrm{angle}=35° \\ \mathrm{second}\mathrm{angle}=90°-35°=55° \end{gathered}$$