Question

Mark the correct alternative in the following question:

Two supplementary angles differ by 40°. The measure of the larger angle is

(a) 70° (b) 80° (c) 110° (d) 100°

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{larger}\mathrm{angle}\mathrm{be}x.\mathrm{Then}, \\ \mathrm{The}\mathrm{smaller}\mathrm{angle}=\left(x-40°\right) \\ \mathrm{As},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{supplementary}\mathrm{angles}\mathrm{is}\mathrm{always}180°. \\ \Rightarrow x+\left(x-40°\right)=180° \\ \Rightarrow 2x-40°=180° \\ \Rightarrow 2x=180°+40° \\ \Rightarrow 2x=220° \\ \Rightarrow x=\frac{220°}{2}\left(\mathrm{By}\mathrm{transposing}2\mathrm{to}\mathrm{RHS}\right) \\ \therefore x=110° \end{gathered}$$

So, the measure of the larger angle is 110°.

Hence, the correct alternative is option (c).