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Gaurav Sood

· started a discussion

· 1 Months ago

Another method (Question: 108561.0 )

Angle made by a chord at the centre is twice the angle made at the circumference so angle OBE =75° and it's supplement is 105°

Question:

In the following figure, AB is the diameter of a circle with centre ‘O’. If ∠AOE = 150°, ∠DAO = 51°, then the measure of ∠CBE will be:


Options:
A) 115°
B) 110°
C) 105°
D) 120°
Solution:
Ans: (c)

OE = OB (radius of circle) \(\Rightarrow\) \(\angle \)OEB = \(\angle \)EBO

\(\angle \)AOE = 150°, then \(\angle \)BOE = 30°

In DBOE,

\(\angle \)BOE + \(\angle \)OEB + \(\angle \)EBO = 180°

\(\Rightarrow\) 30° + 2 \(\angle \)OEB = 180°               (\(\because\)\(\angle \)OEB = \(\angle \)EBO)

\(\Rightarrow\) \(\angle \)OEB = 75°

and \(\angle \)EBC = \(\angle \)BEO + \(\angle \)EOB = 75° + 30° = 105°

Knowledge Expert

· commented

· 1 Months ago

Good Keep it up...

Best wishes
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