Question

In fig, point $Q$ is on the side $MP$ such that $MQ=2$ units and $MP=5.5$ units
Ray $NQ$ is the bisector of $\angle MNP$ of $MNP$. Find $MN:NP$

Answer 1

Given:

$MQ=2$ units and $MP=5.5$ units
Ray $NQ$ is the bisector of $\angle MNP$ of $△MNP$.

It is given that ray $NQ$ is the bisector of $\angle MNP$ of $△MNP$.

Also,
Using Vertical angle bisector theorem: We know that in a triangle, the angle bisector divides the side opposite to the angle in the ratio of the remaining sides.
$\therefore \frac{MQ}{QP}=\frac{MN}{NP}$

$QP=MP-MQ=5.5-2=3.5$

Now, $\frac{MN}{NP}=\frac{2}{3.5}=\frac{4}{7}$

$MN:NP=4:7$