If a transversal intersects two parallel lines, and the difference between two interior angles on the same side of the transversal is 40°, then find the smallest angle among the interior angles.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 70°.
Given that
l and m are parallel linesand P is transversal.
Let the two interior angles on the same side of transversal be x and y Given, their difference is 40º
∴ x − y = 40º
⇒ y = x − 40º ....(i)
Now,
⇒ x + y = 180º
⇒ x + x - 40º = 180º
⇒ 2x = 180º - 40º = 140º
⇒ x = 140º/2 = 70º
Hence, the smaller interior angle is = 70º