If a transversal intersects two parallel lines and the difference of two interior angles on the same side fo a transversal is 20∘ , find the angles.
Let the two interior angles on the same side fo transversal are x and y Given, their difference is 20∘
∴x−y=20∘ ⇒ y=x−20∘ ....(i)
Since l and m are parallel and P is transversal.
Then, x+y=180∘ [∴Sum of an interior angle is 180∘]∴x+x−20∘=180∘ [from Eq.(i)]⇒2x=180∘+20∘⇒2x=200∘⇒x=200∘2=100∘
Therefore, the angles are 100∘ and 80∘ , respectively.