RRB NTPC Mains or Stage 2 Model Paper 8 with solutions

(a) ∠ABC + ∠ADC = 180° (sum of opposites angles of cyclic quadrilateral is 180°)

⇒∠ABC + 110° = 180°( ABCD is a cyclic quadrilateral )
⇒∠ABC = 180 – 110 ⇒∠ABC = 70°(∵AD || BC)
∴ ∠ABC + ∠BAD = 180° (Sum of the interior angles on the same side of tr ansversal is 180°)
70° + ∠BAD = 180°
⇒∠BAD = 180° – 70° = 110°
⇒∠BAC + ∠DAC = 110°
⇒50° + ∠DAC = 110°
⇒∠DAC = 110° – 50° = 60°