SSC CGL 16 Aug 2015 Shift 1 Paper

Sum of all angles of a triangle = 180°
∴ x + 15° + $\frac{6\mathit{x}}{5}$ + 6° + $\frac{2\mathit{x}}{3}$ + 30° = 180°
⇒ x + $\frac{6\mathit{x}}{5}+\frac{2\mathit{x}}{3}$ + 51° = 180°
⇒ $\frac{14\mathit{x}+18\mathit{x}+10\mathit{x}}{15}$
= 180° - 51° = 219°
⇒ 43x = 129 × 15
⇒ x = $\frac{129\times 15}{43}$ = 45°
∴ The angles of triangle are :
x + 15° = 45° + 15° = 60°
$\frac{6\mathit{x}}{5}$ + 6° = $\frac{6\times 45}{5}$ + 6° = 60°
and $\frac{2\mathit{x}}{3}$ + 30° = $\frac{2\times 45}{3}$ + 30°
= 60°
It is an equilateral triangle.