SSC CGL Tier II 21 Sep 2014 Paper

(2) The sum of opposite angles of a concyclic quadrilateral is 180°.
∴ ∠A + C = 180°
⇒ 4x + 5y = 180° ...(i)
∠B + ∠D = 180°
⇒ 7x + y = 180° ...(ii)
By equation (ii) × 5 – (i),
35x + 5y = 900°....(iii)
4x + 5y = 180°....(iv)
By equation (iii) - (iv)
31x = 720
$\mathrm{x}=\frac{720}{31}$
From equation (ii),
7x + y = 180°
$\Rightarrow 7\times \frac{720}{31}+\mathit{y}=180°$
$\Rightarrow \mathit{y}=180-\frac{5040}{31}$
$=\frac{5580-5040}{31}=\frac{540}{31}$
$\therefore \mathit{x}:\mathit{y}=\frac{720}{31}:\frac{540}{31}$
$=4:3$