Question

The angle of a hexagon are $x+{10}^o,2x+{20}^o,2x-{20}^o,3x-{50}^o,x+{40}^o$ and $x+{20}^o$. Find $x$.

Answer 1

Angles of a hexagon are $x+{10}^o,2x+{20}^o$,

$2x-{20}^o,3x-{50}^o,x+{40}^o$ and $x+{20}^o$

$\therefore$ But sum of angles of a hexagon $=(x-2)\times {180}^o$

But sum $=x+10+2x+{20}^o+2x-{20}^o+3x-{50}^o+x+40+x+20$

$=10x+90-70=10x+20$

$\therefore 10x+20={720}^o\Rightarrow 10x=720-20=700$

$\Rightarrow x=\frac{{700}^o}{10}={70}^o$

$\therefore x={70}^o$