Question

Given ABC=65 and BCD=105. Is it possible that Line AB intersects line CD​

Answer 1

Given:

$m\angle ABC=65^\circ$

$m\angle BCD=105^\circ$

To find:

Whether it is possible that Line AB intersects line CD​.

Solution:

We have,

$m\angle ABC=65^\circ$

$m\angle BCD=105^\circ$

The angles $m\angle ABC$ and $m\angle BCD$ are same sided interior angles.

If two lines are parallel and a transversal line intersect them, then the same sided interior angles are supplementary angles and their sum is 180 degrees.

$m\angle ABC+m\angle BCD=65^\circ+105^\circ$

$m\angle ABC+m\angle BCD=170^\circ$

$m\angle ABC+m\angle BCD\neq 180^\circ$

So, the lines AB and CD are not parallel to each other.

Therefore, the intersection of lines AB and CD is possible.