Question

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the smaller of two angles is :

• A. ${72}^{\circ }$
• B. ${108}^{\circ }$
• C. ${54}^{\circ }$
• D. ${36}^{\circ }$

Answer 1

The correct option is A ${72}^{\circ }$

Let the angles be $2x$ and $3x$

Sum of angles on the same side of transversal intersecting two parallel lines is ${180}^{\circ }$

$\Rightarrow 2x+3x={180}^{\circ }\Rightarrow 5x={180}^{\circ }\Rightarrow x={36}^{\circ }$

So the angles are

$2x=2\times {36}^{\circ }={72}^{\circ }3x=3\times {36}^{\circ }={108}^{\circ }$

So the smaller angle is ${72}^{\circ }$