< = ANGLE SIGN
<MO bisects <LMN , m<LMN= 6x – 28, m<LMO = x + 34. Find m<NMO.
Answer choices:
46.4
92.8
63
58
This is not homework or a test, i ofund this in my book. I would like the answer and explanion.
To find the measure of angle NMO, we need to apply the angle bisector theorem. According to the theorem, when a line bisects an angle, it divides the angle into two equal parts.
Let's denote the measure of angle NMO as y.
Since <MO bisects <LMN, we can set up the following equation:
m<LMO + m<NMO = m<LMN
Substituting the given values:
(x + 34) + y = 6x – 28
Simplifying the equation:
x + y + 34 = 6x – 28
Now, let's solve for x:
Subtracting x from both sides:
y + 34 = 5x – 28
Adding 28 to both sides:
y + 34 + 28 = 5x
y + 62 = 5x
Dividing both sides by 5:
(y + 62) / 5 = x
Now that we've found x, we can substitute it back into one of the earlier equations to solve for y.
Let's use the equation:
m<LMO = x + 34
Substituting the value of x:
m<LMO = ((y + 62) / 5) + 34
To find the measure of angle NMO, we need to solve for y in this equation.
Now, let's substitute the given answer choices into this equation to find which one satisfies it.
For each answer choice, plug the value of y into the equation, and check if it holds true:
For option 46.4:
m<LMO = ((46.4 + 62) / 5) + 34 = 78.48
For option 92.8:
m<LMO = ((92.8 + 62) / 5) + 34 = 134.96
For option 63:
m<LMO = ((63 + 62) / 5) + 34 = 108.2
For option 58:
m<LMO = ((58 + 62) / 5) + 34 = 102.8
After checking all the answer choices, we see that none of them satisfies the equation.
Therefore, it appears that there might be an error in the problem or answer choices. It's possible that the correct answer is not provided, or there could be a mistake in the given values. I recommend double-checking the original problem or consulting with your teacher/book for clarification.