The length of segment LP in parallelogram LMNQ is equal to segment PN, which is given as 7 units.
To determine the length of LP in parallelogram LMNQ where the diagonals LN and MQ bisect each other at point P, we will apply the properties of parallelogram and knowledge of geometry.
Given that angle MLQ is 100 degrees and angle PQN is 29 degrees, we can calculate angle LPN as it is supplementary to angle PQN (angles on a straight line add up to 180 degrees).
In parallelogram LMNQ, diagonals LN and MQ bisect each other, so LP equals PN which is given as 7.
So, let's find angle LPN:
Angle LPN = 180 degrees - angle PQN
Angle LPN = 180 degrees - 29 degrees
Angle LPN = 151 degrees
However, because the diagonals bisect each other in a parallelogram, LP must equal PN, so LP is already given as 7 units