Question : In the following figure, AB is the diameter of a circle whose centre is O. If $\angle AOE=150^{\circ},\angle DAO=51^{\circ}$ then the measure of $\angle CBE$ is:
Option 1: 115°
Option 2: 110°
Option 3: 105°
Option 4: 120°
Correct Answer: 105°
Solution :
According to the given figure in question,
Given $\angle$AOE = 150° and $\angle$DAO = 51°
Now, $\angle$EOB + $\angle$AOE = 180°
⇒ $\angle$EOB = 180° – 150° = 30°
Also, OE = OB
⇒ $\angle$OEB = $\angle$OBE = $\frac{150}{2}$ = 75°
⇒ $\angle$CBE = 180° – 75° = 105°
Hence, the correct answer is 105°.
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