In the given figure, \(AOC\) is a straight line. If angle \(AOB=50^\circ\), angle \(AOE=90^\circ\) and angle \(COD=25^\circ\). Find the measures of:

(iv). Reflex angle \(BOD\)

Step : Finding the measure of reflex \(\angle BOD\)

\(\because AOC\) is a straight line.

\(\Rightarrow \angle AOC=180^\circ\)



\(\therefore \angle AOB+\angle BOC=180^\circ\)

\(\Rightarrow 50^\circ+\angle BOC=180^\circ\)

\(\Rightarrow \angle BOC=180^\circ−50^\circ\)

\(\Rightarrow \angle BOC=130^\circ\)

\(\therefore \angle BOC=130^\circ\) and \(\angle COD=25^\circ\)

\(\Rightarrow \angle BOD=\angle BOC+\angle COD \)

\(\Rightarrow \angle BOD= 130^\circ+ 25^\circ=155^\circ\)

Now, reflex angle \(BOD =360^\circ−\angle BOD\)

\(\Rightarrow \) reflex angle \(BOD =360^\circ−155^\circ=205^\circ\)

Hence, reflex angle \(BOD\) is \(205^\circ\).