MCQ
If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $5 : 4$, then the smaller of the two angles is:
- A$120^\circ$
- B$60^\circ$
- ✓$80^\circ$
- D$100^\circ$
✓
Answer
Correct option: C.
$80^\circ$
We know that sum of two interior angles on the same side of a transversal intersecting two parallel lines is $180^\circ .$
Let the common ratio is $x.$
So the angles are$ 5x, 4x.$
So, $5x + 4x = 180^\circ$
$9x = 180^\circ$
$\text{x}=\frac{180^\circ}{9}$
$x = 20^\circ$
So the angles are $5x = 100^\circ .$
$4x = 80^\circ$
So smallest angle is $80^\circ .$
Let the common ratio is $x.$
So the angles are$ 5x, 4x.$
So, $5x + 4x = 180^\circ$
$9x = 180^\circ$
$\text{x}=\frac{180^\circ}{9}$
$x = 20^\circ$
So the angles are $5x = 100^\circ .$
$4x = 80^\circ$
So smallest angle is $80^\circ .$
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