Question

The angles of a quadrilateral are in the ratio 3:4:5:8. 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 3:4:5:8

Let the angles of the quadrilateral be $3x,4x,5x,8x$

Sum of angles of the quadrilateral is ${360}^{\circ }$
$\Rightarrow 3x+4x+5x+8x={360}^{\circ }$
$\Rightarrow 20x={360}^{\circ }$
$\Rightarrow x={18}^{\circ }$

$\therefore 3x={54}^{\circ },4x={72}^{\circ },5x={90}^{\circ },8x={144}^{\circ }$