Question

In the given figure, AOC is a diameter and AC is parallel to ED. If ∠CBE = 64°, calculate ∠DEC.

Answer 1

Join AB,

∠ABC = 90°

(Angle in a semi circle)

∴ ∠ABE = 90° – 64° = 26°

Now, ∠ABE = ∠ACE = 26°

(Angle in the same segment)

Also, AC || ED

∴ ∠DEC = ∠ACE = 26°

(Alternate angles)