AB and CD are straight line segments. ∠ AOE = 50° and ∠ DOB = 95°.
Find the values of the following angles giving a reason for each answer in the comment box.
The diagram is not drawn accurately.
i) obtuse ∠ AOC
ii) acute ∠ BOC
iii) acute ∠ DOE

i) Angle AOC is 95° Reason:- Angle AOC is equal to Angle DOB since they are Vertically Opposite Angles. ii) Angle BOC is 85° Reason:- Angle AOC + Angle BOC - 180° (they lie in a straight line so they are a linear pair. Sum of the angles will be 180°) Angle AOC is 95°, So:- 95° + Angle BOC = 180° Angle BOC= 180° - 95° Angle BOC = 85° iii) Angle DOE is 17° Reason:- Angle AOE+ Angle DOE+ Angle DOB = 180° (they lie in a straight line so they're a linear pair. Sum of the angles will be 180°) So, 68° + Angle DOE+ 95° = 180° 163° + Angle DOE = 180° Angle DOE= 180° - 163° Angle DOE is 17°