Question

In the given figure, l || m and t is a transversal.
If ∠5 = 70°, find the measure of each of the angles
∠1, ∠3, ∠4 and ∠8.

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{l}\parallel \mathrm{m} \\ \mathrm{t}\mathrm{is}\mathrm{a}\mathrm{transversal}. \\ \angle 5=70° \\ \angle 5=\angle 3=70°(\mathrm{alternate}\mathrm{interior}\mathrm{angles}) \\ \angle 5+\angle 8=180°(\mathrm{linear}\mathrm{pair}) \\ \mathrm{or}70°+\angle 8=180° \\ \angle 8=110° \\ \angle 1=\angle 3=70°(\mathrm{vertically}\mathrm{opposite}\mathrm{angles}) \\ \angle 3+\angle 4=180°(\mathrm{linear}\mathrm{pair}) \\ \mathrm{or}\angle 4=180-\angle 3=180-70=110° \end{gathered}$$