Question

Assertion : If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the greater of the two angles is 100. Reason : If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180.​

Answer 1

Answer:

Both Assertion (A) ans Reason (R) are true and (R) is the correct explanation of (A)

Explanation:

let the ratio be 5x and 4x.

According to reason , sum of interior angles on the same side of transversal side is 180°

after putting the values in we got,

5x + 4x = 180°

9x = 180°

x = 180/9 = 20°

5x = 5 × 20° = 100° ( as given, one of the greater of the two angle is 100°)

4x = 4 × 20 = 80°

hope this answer helps you dear....take care!

Answer 2

Given : Assertion : If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the greater of the two angles is 100°.

Reason : If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180°.​

To Find : Comment on Assertion and reason

Solution:

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent.  

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Co-Interior angles are supplementary. ( adds up to 180°)

two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5:4

Let say one angle =5a

then second angle would be 4a

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

=> 5a + 4a = 180°

=> 9a = 180°

=> a = 20°

Hence one angle =100° and other = 80°

so greater of the two angles is 100°

Hence Assertion is TRUE

Reason : If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180.​

TREU

Both Assertion and reason are TRUE and Reason is the correct explanation of the assertion.

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