Question

The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle.

Answer 1

Sum of all interior angles of a quadrilateral = ${360}^{\circ }$
let the angles of the quadrilateral be $2x^{\circ },3x^{\circ },5x^{\circ }and8x^{\circ }.$
2x + 3x + 5x + 8x = ${360}^{\circ }$
$\Rightarrow 18x={360}^{\circ }\Rightarrow x={20}^{\circ }$
Hence the angles are
$2\times 20={40}^{\circ },3\times 20={60}^{\circ },5\times 20={100}^{\circ }and8\times 20={160}^{\circ }.$