Question

Question 96

If a transversal intersects two parallel lines and the difference of two interior angles on the same side fo a transversal is ${20}^{\circ }$ , find the angles.

Answer 1

Let the two interior angles on the same side fo transversal are x and y Given, their difference is ${20}^{\circ }$
$\therefore x-y={20}^{\circ }\Rightarrow y=x-{20}^{\circ }....\left(i\right)$
Since l and m are parallel and P is transversal.

Then, $x+y={180}^{\circ }[\therefore Sumofaninteriorangleis{180}^{\circ }]\therefore x+x-{20}^{\circ }={180}^{\circ }[fromEq.(i\left)\right]\Rightarrow 2x={180}^{\circ }+{20}^{\circ }\Rightarrow 2x={200}^{\circ }\Rightarrow x=\frac{{200}^{\circ }}{2}={100}^{\circ }$
Now, $y=x-{20}^{\circ }\therefore y={100}^{\circ }-{20}^{\circ }={80}^{\circ }$

Therefore, the angles are ${100}^{\circ }$ and ${80}^{\circ }$ , respectively.