Question

The four angles of a quadrilateral are in the ratio $2:3:4:6$. Find the measures of each angle

Answer 1

The ratio of the angles is $2:3:4:6$

To find: The measures of each angle.

Observe that $2+3+4+6=15$.

Thus $15$ parts accounts for ${360}^{\circ }$

Hence, $15$ parts = ${360}^{\circ }$

$2$ parts = ( ${360}^{\circ }$/$15)\times$ $2$ = ${48}^{\circ }$

$3$ parts = (${360}^{\circ }$/$15)\times$ $3$ = ${72}^{\circ }$

$4$ parts = ( ${360}^{\circ }$ /$15)\times$ $4$ = ${96}^{\circ }$

$6$ parts = ( ${360}^{\circ }$/$15)\times$ $6$ = ${144}^{\circ }$

Thus the angles are ${48}^{\circ }$ ${72}^{\circ }$, ${96}^{\circ }$ ${144}^{\circ }$