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Given LMO = 8x – 14 and NMO = 2x + 34, what is the measure of angle LMN?

A) 6x + 20
B) 10x + 48
C) 10x - 20
D) 6x - 48

User Ufx
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1 Answer

3 votes

Final answer:

The measure of angle LMN is found by adding the measures of angles LMO and NMO, given by the expressions 8x - 14 and 2x + 34 respectively. They form a linear pair that equals 180 degrees. Simplifying yields the expression 10x + 20 equals 180, which, once solved for x, indicates that option (C) 10x - 20 is the correct answer.

Step-by-step explanation:

To find the measure of angle LMN, we need to recognize that LMO and NMO form a linear pair if LMN is the angle formed by the two lines meeting at point M. Since LMO and NMO are on a straight line, their measures should add up to 180 degrees (straight angle). We are given the measures of angles LMO and NMO in terms of x.

LMO = 8x – 14
NMO = 2x + 34

To find LMN, let's add LMO and NMO and set them equal to 180 degrees:

8x - 14 + 2x + 34 = 180

Combining like terms:

10x + 20 = 180

We solve this equation by subtracting 20 from both sides:

10x = 160

And then dividing both sides by 10 to solve for x:

x = 16

Since the question asks for the measure of angle LMN in terms of x, the correct answer is the one that has a coefficient of 10 in front of x since we established that LMO + NMO = 10x + 20.

Therefore, the measure of angle LMN is 10x - 20, answering it as (C) 10x - 20.

User Steven Miller
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