Question

The four angles of a quadrilateral are as 3:5:7:9. Find the angles.

Answer 1

Sum of four angles of a quadrilateral ${360}^{\circ }$and ratio in angles = 3:5:7:9
Let first angles = 3x
Then second angle=5x
third angle=7x
and fourth angle=9x
$\therefore 3x+5x+7x+9x={360}^{\circ }\Rightarrow 24x={360}^{\circ }\Rightarrow x=\frac{{360}^{\circ }}{24}={15}^{\circ }$
$\therefore$ First angle =3x= $3\times {15}^{\circ }={45}^{\circ }$
Second angle =5x= $5\times {15}^{\circ }={75}^{\circ }$
third angle =7x= $7\times {15}^{\circ }={105}^{\circ }$
and fourth angle=9x= $9\times {15}^{\circ }={135}^{\circ }$