Question

In figure, line $XY\parallel PQ$ and we have $\angle MLY = 2\angle LMQ$, find $\angle LMQ$

Answer 1

Hint: In order to solve the question we have to apply the concept of co-interior angles, which means two interior angles on the same side of the transversal and the sum of these two angles equals to ${180^ \circ }$.

Complete step-by-step solution:
It is stated in the question that $XY\parallel PQ$ so the sum of the co-interior angles will be equal to $180_{}^0$
Therefore we can write, $\angle MLY + \angle LMQ = {180^ \circ }$
Putting the value of $\angle MLY = 2\angle LMQ$ in the above equation we get-
$\angle 2LMQ + \angle LMQ = {180^ \circ }$
Now by doing addition we get-
So, $3\angle LMQ = {180^ \circ }$
By division we get-
Thus, $LMQ = {60^ \circ }$

Hence the value of $LMQ = {60^ \circ }$

Note: Where a transversal intersects two parallel lines, the corresponding angles become equal, the vertically opposite angles are also equal, the alternate exterior and interior angles are also equal and the sum of the interior angles on the same side of the transversal which is known as co-interior angles equals to \[{180^ \circ }\].