Question

The angles of a quadrilateral are x°, (x-10)°, (x+ 30)° and 2x°. Then find the value of the greatest angle.

• A. ${68}^0$
• B. ${136}^0$
• C. ${180}^0$
• D. ${98}^0$

Answer 1

The correct option is B ${136}^0$

We know that the sum of all angles in a quadrilateral is 360${}^{\circ }$.
Then, $x^{\circ }+(x-10{)}^{\circ }+(x+30{)}^{\circ }+(2x{)}^{\circ }={360}^{\circ }$
$5x^{\circ }+{20}^{\circ }={360}^{\circ }$
$x=\frac{340}{5}={68}^{\circ }$
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 $={136}^{\circ }$