Question

The angles of a hexagon are $(2x+5{)}^o,(3x-5{)}^o,(x+40{)}^o,(2x+20{)}^o,(2x+35{)}^o$. Find the value of $x$.Hence find the angles.

Answer 1

We know that Sum of all angles of a hexagon$={720}^{\circ }$

$\Rightarrow 2x+5+3x-5+x+40+2x+20+2x+35={720}^{\circ }$

$\Rightarrow 10x+{95}^{\circ }={720}^{\circ }$

$\Rightarrow 10x={720}^{\circ }-{95}^{\circ }={625}^{\circ }$

$\therefore x=\frac{{625}^{\circ }}{10}={62.5}^{\circ }$

Hence the angles are:

$2x+5=2\times 62.5+5={130}^{\circ }$

$3x-5=3\times 62.5-5={182.5}^{\circ }$

$x+40=62.5+40={102.5}^{\circ }$

$2x+20=2\times 62.5+20={145}^{\circ }$

$2x+35=2\times 62.5+35={160‬}^{\circ }$