∠LMN and ∠NMO are a linear pair of angles. If ∠LMN = 4x + 3 and ∠NMO = 10x – 5, then find the value of x.
(1 point)
Responses
x = 10
x = 10
x = 12
x = 12
x = 14
x = 14
x = 13
To solve this problem, we need to use the property of a linear pair, which states that the sum of the angles in a linear pair is 180 degrees.
Since ∠LMN and ∠NMO are a linear pair, we have the equation:
∠LMN + ∠NMO = 180
Substituting the given expressions, we get:
4x + 3 + 10x - 5 = 180
Combining like terms, we have:
14x - 2 = 180
Adding 2 to both sides, we get:
14x = 182
Dividing both sides by 14, we find that:
x = 13
So, the value of x is 13.