Question

in the figure, lmno is a parallelogram. what is the measure of ∠x?

Explanation:

Step1: Recall property of parallelogram

In parallelogram $LMNO$, $\angle L=\angle NOM + \angle LMO$. Since $\angle L = 92^{\circ}$, $\angle NOM=53^{\circ}$ and $\angle LMO = 35^{\circ}$, this property holds. Also, $\angle ONM$ and $\angle L$ are opposite - angles of the parallelogram, so $\angle ONM=\angle L = 92^{\circ}$.

Step2: Use linear - angle property

$\angle x$ and $\angle ONM$ are linear - pair angles. A linear pair of angles sums up to $180^{\circ}$. Let $\angle ONM = y$, then $\angle x=180^{\circ}-y$.

Step3: Calculate the value of $\angle x$

Since $y = 92^{\circ}$, then $\angle x=180 - 92=88^{\circ}$.

Answer:

$88^{\circ}$