Mathematics

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

In the given figure, AOC is a diameter and AC is parallel to ED. If ∠CBE = 64°, calculate ∠DEC. Circles, Concise Mathematics Solutions ICSE Class 10.

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In the given figure, AOC is a diameter and AC is parallel to ED. If ∠CBE = 64°, calculate ∠DEC. Circles, Concise Mathematics Solutions ICSE Class 10.

∠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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