Question

In the given figure, two straight line AB and CD intersect at a point O.
If ∠AOC = 42°, find the measure of each of the angles:


(i) ∠AOD
(ii) ∠BOD
(iii) ∠COB

Answer 1

AB and CD intersect at O and CD is a straight line.

$$\begin{gathered} \left(\mathrm{i}\right)\angle \mathrm{COA}\hspace{0.17em}+\angle \mathrm{AOD}=180°(\mathrm{linear}\mathrm{pair}) \\ 42°+\angle \mathrm{AOD}=180° \\ \angle \mathrm{AOD}=138° \\ \left(\mathrm{ii}\right)\angle \mathrm{COA}\mathrm{and}\angle \mathrm{BOD}\mathrm{are}\mathrm{vertically}\mathrm{opposite}\mathrm{angles}. \\ \therefore \angle \mathrm{COA}=\angle \mathrm{BOD}=42°[\mathrm{from}(\mathrm{i}\left)\right] \\ \left(\mathrm{iii}\right)\angle \mathrm{COB}\mathrm{and}\angle \mathrm{AOD}\mathrm{are}\mathrm{vertically}\mathrm{opposite}\mathrm{angles}. \\ \therefore \angle \mathrm{COB}=\angle \mathrm{AOD}=138°[\mathrm{from}(\mathrm{i}\left)\right] \end{gathered}$$