In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE = 65°, then what is the value of ∠DEC?
Explanation:
m∠EBC = 65°
∴ m∠EOC = 130° (∵ angle subtended by an arc at the centre is twice the angle subtended by the same arc on the circumference)
As AC || ED, m∠OCE = m∠DEC
ΔOEC is an isosceles triangle.
∴ m∠OCE = m∠OEC = (180 – 130)/2 = 25°
∴ m∠DEC = 25°
Hence, option (d).
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