CDS Model Paper 2 Mathematics

Let the line m cut AB and CD at point P and Q respectively
∠DOQ=x (exterior angle)
Hence, Y+2x (corresponding angle)
∴ y=x ...(i)
Also ∠DOO=x (vertically opposite angles)
In ΔOCD, sum of the angles =180°
∴ y+2y+2x+x=180°
3x+3y=180°
x+y=60 ...(ii)
From (i) and (ii) x=y=30=2y=60
∴ ∠ODS=180−60=120°
∴ θ=180−3x=180−3(30)=180−90=90°.
∴ The required ratio =90:120=3:4.