In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If angle CBE = 45°, then what is the value of angle DEC?
Explanation:
In the given figure if we join AB then ∠ABC = 90°. [Angle subtended by diameter AC on circle is right angle.]
∴ ∠ABE + ∠EBC = 90°
⇒ ∠ABE = 90° - 45° = 45°
Now, if we consider chord AE, angle it subtends at point B on circle will be same as the angle it subtends at point C on the circle.
⇒ ∠ABE = ∠ACE = 45°
Now, AC and ED are parallel
⇒ ∠ACE = ∠CED = 45° [alternate interior angles]
Hence, option (a).
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