ABCD is a cyclic quadrilateral The side AB is extended to E in such a way that BE BC If ang ADC 70 d...........

Quantitative Aptitude ( CCS) Geometry

ABCD is a cyclic quadrilateral. The side AB is extended to E in such a way that BE = BC. If ∠ADC = 70°, ∠BAD = 95°, then ∠DCE is equal to

140°

120°

165°

110°

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Explanation:

Given, ∠ADC = 70° and ∠BAD = 95°
∠ADC + ∠ABC = 180°
∠ABC = 180° – ∠ADC = 180° – 70° = 110°
∴ ∠CBE = 180° – ∠ABC = 180° – 110° = 70°
BC = BE (given)
∴ ∠BEC = ∠BCE
In ΔBCE, we know that
∠BCE + ∠BEC + ∠CBE = 180°
2∠BCE = 180° – ∠CBE = 180° – 70° = 110°
∠BCE = 55° = ∠BEC
∠BAD + ∠BCD = 180°
∠BCD = 180° – ∠BAD = 180° – 95° = 85°
∴ ∠DCE = ∠BCD + ∠BCE = 85° + 55° = 140°