Question

The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.

• A. ${40}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$, ${140}^{\circ }$
• B. ${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$
• C. ${30}^{\circ }$, ${40}^{\circ }$, ${50}^{\circ }$, ${60}^{\circ }$
• D. ${10}^{\circ }$, ${20}^{\circ }$, ${30}^{\circ }$, ${40}^{\circ }$

Answer 1

The correct option is B

${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$

The angles of a quadrilateral are in the ratio 3:4:5:6.

Let the angles of the quadrilateral be $3x,4x,5x,6x$.

The sum of the angles of a quadrilateral is ${360}^{\circ }$.
$\Rightarrow 3x+4x+5x+6x={360}^{\circ }$
$\Rightarrow 18x={360}^{\circ }$
$\Rightarrow x={20}^{\circ }$

$\therefore 3x={60}^{\circ },4x={80}^{\circ },5x={100}^{\circ },6x={120}^{\circ }$