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.

• A. ${136}^{\circ }$
• B. ${180}^{\circ }$
• C. ${68}^{\circ }$
• D. None of these

Answer 1

The correct option is A

${136}^{\circ }$

$\text{Sum of the angles of a Quadrilateral}={360}^{\circ }$
We have
$x^{\circ }+(x-10{)}^{\circ }+(x+30{)}^{\circ }+(2x{)}^{\circ }={360}^{\circ }$
$5x+20=360$
$x=\frac{340}{5}={68}^{\circ }$
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 $={136}^{\circ }$