Question

The angles of a quadrilateral are $x^{\circ },(x-10{)}^{\circ },(x+30{)}^{\circ }$ and $(2x{)}^{\circ }$. Find the value of the greatest angle. (2 marks)

Answer 1

By angle sum property, sum of angles of a quadrilateral will be 360°.
Given the angles are
$x,(x-10)°,(x+30)°$ and $2x$° .

$\Rightarrow x+(x-10)+(x+30{)}^{\circ }+(2x{)}^{\circ }=360°$
$\Rightarrow$ $5x+20°=360$
$\Rightarrow$ $5x=360°-20°=340°$
$\Rightarrow$ $x=\frac{340}{5}={68}^{\circ }$ (1 mark)

The angles are ${68}^{\circ },{68}^{\circ }-{10}^{\circ },{68}^{\circ }+{30}^{\circ },2\times {68}^{\circ }$

$i.e.{68}^{\circ },{58}^{\circ },{98}^{\circ },{136}^{\circ }.$

$\therefore$ Greatest angle $={136}^{\circ }$ (1 mark)