Question

In the given figure, two straight line PQ and RS intersect at a O.
If ∠POS = 114°, find the measure of each of the angles:

(i) ∠POR
(ii) ∠ROQ
(iii) ∠QOS

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\angle \mathrm{POS}+\angle \mathrm{POR}=180°(\mathrm{linear}\mathrm{pair}) \\ \mathrm{or}114°+\angle \mathrm{POR}=180° \\ \mathrm{or}\angle \mathrm{POR}=180°-114°=66° \\ \left(\mathrm{ii}\right)\mathrm{Since}\angle \mathrm{POS}\mathrm{and}\angle \mathrm{QOR}\mathrm{are}\mathrm{vertically}\mathrm{opposite}\mathrm{angles},\mathrm{they}\mathrm{are}\mathrm{equal}. \\ \therefore \angle \mathrm{QOR}=114° \\ \left(\mathrm{iii}\right)\mathrm{Since}\angle \mathrm{POR}\mathrm{and}\angle \mathrm{QOS}\mathrm{are}\mathrm{vertically}\mathrm{opposite}\mathrm{angles},\mathrm{they}\mathrm{are}\mathrm{equal}. \\ \therefore \angle \mathrm{QOS}=66° \end{gathered}$$