Question

In following figure , chord ED is parallel to the diameter AC of the circle. Given ∠ CBE = 65° , calculate ∠DEC .

Answer 1

Let O be the centre of the cirde on diameter AC of the circle

Since, EC make ∠ EOC at the centre and ∠ EBC on the remaining part of the circle

∴ ∠ EOC = 2 ∠EBC = 2 (65) = 130°

In Δ EOC ,

∠EOC + ∠ OCE + ∠ CEO =  180°

130 + x + x = 180°  (OE = OC , ∴ ∠ OEC = ∠ OCE = x)

2x = 50

x = 25

∠ OCE = ∠ OEC  = 25°

Also , ∠ OCE = ∠ CED = 25°   (alternate interior angles)