Question

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

• A. ${145}^{\circ }$, ${105}^{\circ }$, ${65}^{\circ }$, ${45}^{\circ }$
• B. ${135}^{\circ }$, ${105}^{\circ }$, ${75}^{\circ }$, ${45}^{\circ }$​
• C. ${35}^{\circ }$, ${65}^{\circ }$, ${95}^{\circ }$, ${125}^{\circ }$​
• D. ${15}^{\circ }$, ${105}^{\circ }$, ${130}^{\circ }$, ${40}^{\circ }$​

Answer 1

The correct option is B

${135}^{\circ }$, ${105}^{\circ }$, ${75}^{\circ }$, ${45}^{\circ }$​

Let the angles of the quadrilateral will be $3x^{\circ }$, $5x^{\circ }$, $7x^{\circ }$, $9x^{\circ }$.
Sum of the angles of a quadrilateral = ${360}^{\circ }$

$\Rightarrow {360}^{\circ }=3x+5x+7x+9x$
$\Rightarrow 24x={360}^{\circ }$

$\therefore x=\frac{{360}^{\circ }}{24}={15}^{\circ }$
$\therefore 3x={45}^{\circ },5x={75}^{\circ },7x={105}^{\circ },9x={135}^{\circ }$