Question

Mark the correct alternative in the following question:

Two complementary angles differ by 20°. The smaller angle is

(a) 55° (b) 25° (c) 65° (d) 35°

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{smaller}\mathrm{angle}\mathrm{be}x.\mathrm{Then}, \\ \mathrm{The}\mathrm{larger}\mathrm{angle}=\left(x+20°\right) \\ \mathrm{As},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{complementary}\mathrm{angles}\mathrm{is}\mathrm{always}90°. \\ \Rightarrow x+\left(x+20°\right)=90° \\ \Rightarrow 2x+20°=90° \\ \Rightarrow 2x=90°-20° \\ \Rightarrow 2x=70° \\ \Rightarrow x=\frac{70°}{2}\left(\mathrm{By}\mathrm{transposing}2\mathrm{to}\mathrm{RHS}\right) \\ \therefore x=35° \end{gathered}$$

So, the smaller angle is 35°.

Hence, the correct alternative is option (d).