Question

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

Answer 1

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let the angles be 2x and 3x , Now

2x + 3x = 5x

5x = 180  ( since interior angles on the same side of a transversal = 180 degrees )

x = 180/5

x = 36

greater angle is 3x = 3 * 36 = 108

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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