MCQ
If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $2 : 3$, then the greatest of two angles is:
- A$36^\circ $
- ✓$108^\circ$
- C$72^\circ$
- D$54^\circ$
✓
Answer
Correct option: B.
$108^\circ$
Let a and b are two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $2 : 3$ and we know that If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.Let common ratio is $x,$
$a = 2x$ and $b = 3x$
$a + b = 180^\circ$
$2x + 3x = 180^\circ$
$5x = 180^\circ$
$\text{x} = \frac{180^\circ}{5} = 36^\circ$
$x = 36^\circ$
$3x = 3 \times 36^\circ = 108^\circ .$
$a = 2x$ and $b = 3x$
$a + b = 180^\circ$
$2x + 3x = 180^\circ$
$5x = 180^\circ$
$\text{x} = \frac{180^\circ}{5} = 36^\circ$
$x = 36^\circ$
$3x = 3 \times 36^\circ = 108^\circ .$
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