∠LMN and ∠NMO are a linear pair of angles. If ∠LMN = 4x + 3 and ∠NMO = 10x – 5, then find the value of x.
Since ∠LMN and ∠NMO are a linear pair of angles, their sum is 180 degrees.
Thus, we have the equation: ∠LMN + ∠NMO = 4x + 3 + 10x - 5 = 180
Simplifying the equation, we get: 14x - 2 = 180
Adding 2 to both sides, we have: 14x = 182
Dividing both sides by 14, we get: x = 13
Therefore, the value of x is 13.