Hello there. To solve this question, we have to remember some properties about angles.
Given the following diagram:
We know that:
[tex]\angle LON=152^{\circ}[/tex]
And the image shows that
[tex]\angle LOM=78^{\circ}[/tex]
We want to determine the measure of
[tex]\angle MON[/tex]
That is, the following angle in blue:
For this, notice that
[tex]\angle LOM+\angle MON=\angle LON[/tex]
Therefore we found an equation that can give us the answer.
Plugging the values, we have that
[tex]78^{\circ}+\angle MON=152^{\circ}[/tex]
Subtract 78º on both sides of the equation.
[tex]\angle MON=152^{\circ}-78^{\circ}=74^{\circ}[/tex]
This is the measure in degrees that we're looking for.
