Question

∠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)

x = 10
x = 12
x = 14
x = 13

Answer 1

Answer: x = 13

Step-by-step explanation:

Given: ∠LMN and ∠NMO are a linear pair of angles.

We know that linear pair of angles are supplementary.

Then ∠LMN + ∠NMO=180°

If ∠LMN = $4x+3$ and ∠NMO = $10x-5$,

$\Rightarrow4x+3+10x-5=180$

$\Rightarrow14x-2=180\\\Rightarrow14x=180+2\\\Rightarrow14x=182\\\Rightarrow\ x=\frac{182}{14}\\\Rightarrow\ x=13$

Hence, the value of x=13 .

Answer 2

The value of x is 13

The sum of linear pair sums up to 180 degrees. This shows that:

• ∠LMN  +  ∠NMO = 180

Given the following parameters:

• ∠LMN = 4x + 3
• ∠NMO = 10x – 5

Taking the sum and equating to 180 degrees

4x + 3 + 10x - 5  = 180

14x - 2 = 180

14x = 180 + 2

14x = 182

x = 182/14

x = 13

Hence the value of x is 13

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