ABCD is a cyclic quadrilateral. The side AB is extended

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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

1. 140°
2. 120°
3. 165°
4. 110°

Correct Option: A

According to question , we draw a figure of cyclic quadrilateral ABCD in which side AB is extended to E in such a way that BE = BC ,

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

∴ ∠ BCE = ∠ BEC =	110	= 55°
	2

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