MCQ
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 :
- ✓$72^\circ $
- B$108^\circ$
- C$54^\circ$
- D$36^\circ$
✓
Answer
Correct option: 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 $
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