Question

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

Answer 1

Ratio of four angles of a quadrilaterla = 3:5:7:9
Let these angles be 3x, 5x, 7x and 9x
then 3x + 5x + 7x+ 9x = ${360}^0$ (sum of angles)
$\Rightarrow 24x={360}^0\Rightarrow x=\frac{{360}^0}{24}={15}^0$
$\therefore$ First angle = $3x=3\times {15}^0={45}^0$
Second angle = $5x=5\times {15}^0={75}^0$
Third angle = $7x=7\times {15}^0={105}^0$
Fourth angle = $9x=9\times {15}^0={135}^0$