Question

In the adjoining fig . 1.71, line l $\parallel$ line m and line p is the transversal.
if r = 20$°$ then find a:b.

Answer 1

Given: $l\parallel m;p\mathrm{is}\mathrm{the}\mathrm{transversal}\mathrm{and}r=20°$

$$\begin{gathered} \mathrm{Here},a=r(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}) \\ \Rightarrow a=20° \\ \mathrm{Also},a+b=180°(\mathrm{Interior}\mathrm{angles}\mathrm{on}\mathrm{the}\mathrm{same}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{transversal}\mathrm{of}\mathrm{two}\mathrm{parallel}\mathrm{lines}\mathrm{are}\mathrm{supplementary}) \\ \Rightarrow 20°+b=180° \\ \Rightarrow b=160° \\ \mathrm{Now},a:b=20°:160° \\ \therefore a:b=1:8 \end{gathered}$$