Question

Given that segment AB and CD are parallel, if lines l, m and n interesect at point O. Find the ratio of $\theta$ to $\angle ODS$.

• A. 2 : 3
• B. 3 : 2
• C. 3 : 4
• D. Data insufficient

Answer 1

The correct option is C 3 : 4

Let the line m cut AB and CD at point P and Q respectively
$\angle DOQ=x$ (exterior angle)
Hence, y + 2x (corresponding angle)
$\therefore y=x$
Also. $\angle DOQ=x$ (vertically opposite angles)
In $\Delta OCD,$ sum of the angles = ${180}^{\circ }$
$\therefore y+2y+2x+x={180}^{\circ }3x+3y={180}^{\circ }x+y=60From\left(1\right)and\left(2\right)x=y=30=2y=60\therefore \angle ODS=180-60={120}^{\circ }\therefore \theta =180-3x=180-3\left(30\right)=180-90={90}^{\circ }$
$\therefore$ The required ratio = 90 : 120 = 3 : 4.