Question

The angles of a quadrilateral are in the ratio 1: 2 : 3 : 4. The angles of the quadrilateral are respectively ____.

• A. ${144}^{\circ }$, ${108}^{\circ }$, ${60}^{\circ }$, ${48}^{\circ }$
• B. ${36}^{\circ }$, ${72}^{\circ }$, ${108}^{\circ }$, ${144}^{\circ }$​
• C. ${30}^{\circ }$, ${60}^{\circ }$, ${90}^{\circ }$, ${120}^{\circ }$​
• D. ${10}^{\circ }$, ${20}^{\circ }$, ${30}^{\circ }$, ${40}^{\circ }$​

Answer 1

The correct option is B

${36}^{\circ }$, ${72}^{\circ }$, ${108}^{\circ }$, ${144}^{\circ }$​

Let the smallest angle of quadrilateral be $x^{\circ }$.
Then, the angles of the quadrilateral will be $x^{\circ }$, $2x^{\circ }$, $3x^{\circ }$ and $4x^{\circ }$.
Sum of the angles of a quadrilateral is ${360}^{\circ }$.
$\Rightarrow {360}^{\circ }=x+2x+3x+4x$
$\Rightarrow 10x={360}^{\circ }$
$\therefore x={36}^{\circ },2x={72}^{\circ },3x={108}^{\circ }and4x={144}^{\circ }$