SSC CGL 19 Oct 2014 Shift 2 Paper

Question : 140 of 200

Marks: +1, -0

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°

Validate

Solution:

In concyclic quadrilateral ABCD,
∠ ADC + ∠ ABC = 180°
⇒ 70° + ∠ ABC = 180°
∴ ∠ ABC = 180° – 70° = 110°
∴ ∠ CBE = 180° – 110° = 70°
BC = BE
∴ ∠ BCE = ∠ BEC =

{110°}/2

= 55°
∠ BAD = 95°
∴ ∠ BAD + ∠ BCD = 180°
⇒ ∠ BCD = 180° – 95° = 85°
∴ ∠ DCE = ∠ BCD + ∠ BCE
= 85° + 55° = 140°

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