Question

If two interior angles on the same side of a transversal intersecting two parallel lines in the ratio 2:3 then finf the larger of two angles.

Answer 1

Let the two angles be 'a' and 'b'.
a + b = 180° (Co-interior angles) →1
Now, They're in the ratio 2 : 3
∴a=2x
  b=3x
Substituting in 1, we get:
2x + 3x = 180°
        5x = 180°
         x = 180° ÷ 5
       ⇒x = 36°.

We know that the larger angle is 3x (As 3x>2x)
3x = 3(36°)
     =108°

∴The larger of the two angles will be 108°.


Hope this helps..

Answer 2

Two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3 ....(Given)  

Let one angle = 2x  

Other angle = 3x

As sum of interior angles on same side of transversal intersecting two parallel line is 180

⇒2x = 3x = 180

⇒5x = 180

⇒x =  180 / 5  =36  

Hence, two angles are 2x = 2 × 36 = 72

⇒3x = 3 × 36 = 108  

Hence, greater angle is 108