Advertisement Remove all ads

If Two Interior Angles on the Same Side of a Transversal Intersecting Two Parallel Lines Are in the Ratio 2:3, Then the Measure of the Larger Angle is - Mathematics

MCQ

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the measure of the larger angle is

Options

  •  54°

  •  120°

  •  108°

  •  136°

Advertisement Remove all ads

Solution

Let us draw the following figure:

Here AB || CD with t as a transversal.

Also, ∠1and ∠2are the two angles on the same side of the transversal.

It is given that

∠1:∠2 = 2:3

Therefore, let

∠1 = 2x 

and ∠2 = 3x

We also, know that, if a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.

Therefore,

∠1 + ∠2 = 180°

On substituting ∠1 =2x  and ∠2 = 3x in equation above, we get:

2x +3x = 180°

       5x = 180°

         `x = (180°) /5`

         x = 36°

Clearly, 3x >2x

Therefore, 

∠2 > ∠1

Also,

∠2 = 3x 

∠2 = 3(36°)

∠2 = 108°

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Q 10 | Page 53
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×