Answer:
40°
Explanation:
You want the measure of ∠LNO, marked as y°, given the two vertical angle pairs {100°, (x -y)°} and {y°, 2/7x°}.
Vertical angles
Vertical angles have the same measure, so we can write the equations ...
Solution
We want the value of y, so it makes sense to solve these equations using a method that eliminates x. Rewriting the second equation to solve for x, we have ...
x° = 7/2y°
Substituting this into the first equation gives ...
100° + (7/2y -y)°
100° = 5/2y°
2/5(100) = y° = 40°
The measure of ∠LNO is 40°.