Question

The angles of a quadrilateral are in the ratio $3:5:9:13$. Find all the angles of the quadrilateral in degrees.

• A. $36,60,108,156$
• B. $36,70,108,156$
• C. $36,60,118,156$
• D. none of the above

Answer 1

Answer: (A)

$36,60,108,156$

Let the four angles of the quadrilateral be $3x,5x,9x$ and $13x$
$3x+5x+9x+13x={360}^{\circ }$
[sum of all angles of the quadrilateral is ${360}^{\circ }$]
$30x={360}^{\circ }$
$x={12}^{\circ }$
Hence, the angles of the quadrilateral are $3\times {12}^{\circ }={36}^{\circ },5\times {12}^{\circ }={60}^{\circ },9\times {12}^{\circ }={108}^{\circ }$ and $13\times {12}^{\circ }={156}^{\circ }$