Question

The angles of a quadrilateral are in the ratio 1:2:5:7. The angles of the quadrilateral are:

• A. 40°, 100°, 80°, 140°
• B. 60°, 80°, 100°, 120°
• C. 30°, 40°, 50°,60°
• D. 10°, 20°, 30°, 40°

Answer 1

The correct option is B

60°, 80°, 100°, 120°

The angles of a quadrilateral are in the ratio 1:2:5:7.

Let the angles of the quadrilateral be $x,2x,5x,7x$

Sum of angles of the quadrilateral is ${360}^{\circ }$
$\Rightarrow x+2x+5x+7x={360}^{\circ }$
$\Rightarrow 15x={360}^{\circ }$
$\Rightarrow x={24}^{\circ }$

$\therefore x={24}^{\circ },2x={48}^{\circ },5x={120}^{\circ },7x={168}^{\circ }$