Mathematics
In the given figure, AOC is a diameter and AC is parallel to ED. If ∠CBE = 64°, calculate ∠DEC.
Circles
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Answer
Join AB.
∠ABC = 90° [As angle in a semi-circle is a right angle.]
From figure,
∠ABE = ∠ABC - ∠CBE = 90° - 64° = 26°.
As angles in same segment are equal.
∠ACE = ∠ABE = 26°.
Given,
AC || ED
∴ ∠DEC = ∠ACE = 26° [Alternate angles are equal]
Hence, ∠DEC = 26°.
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