Points A, D, C, B and E are concyclic. If ∠AEC = 50° and ∠ABD = 30°, then what is the measure(in degrees) of ∠CBD?
Explanation:
ADCE is a cyclic quadrilateral, so opposite angles are supplementary.
⇒ ∠ADC + ∠AEC = 180°
⇒ ∠ADC + 50° = 180°
⇒ ∠ADC = 130°
ABCD is a cyclic quadrilateral, so opposite angles are supplementary.
⇒ ∠ABC + ∠ADC = 180°
⇒ x + 30° + 130° = 180°
= x = 20°
⇒ ∠CBD = x = 20°
Hence, the correct answer is Option A
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