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1. MO bisects LMN, LMN = 5x-23, LMO = x+32. Find NMO.
>>I got the answer 45.75 but I got it wrong. I do not know how to solve this question and I have tried all that I know. Please help..

  • Geometry -

    What is LMN? For example, is this a line segment, triangle, or ?

    How did you get 45.75?

    You need to post a better explanation.

    Think of it like this. If you knew absolutely nothing about this problem could you solve it with just the info you posted?

  • Geometry -

    LMN is a Line segment and MO bisect. So it looks like the letter "V" but with a line straight through the middle going up and down.

  • Geometry -

    I agree with "helper".
    I cannot figure out what you mean by
    LMO = x+32
    LMO cannot be a line segment the way you described it.
    Is it angle(LMO) = x + 32 ?
    What does MO bisect?
    Where is O ?
    Are the angles at M right angles?

  • Geometry -

    Let Me Rephrase This:

    RayMO bisects AngleLMN,
    The Measure of AngleLMN =5x-23,
    The Measure of LMO = x+3,
    O is the point is from RayMO, the point when a bisect is made.
    Find AngleNMO.

  • Geometry -

    Thank you. That's much better.
    If I am understanding your description,

    A line that bisects an angle divides it into two congruent parts.

    Therefore, angle LMO = angle NMO

    angle NMO = angle LMN - angle LMO
    angle NMO = 5x - 23 - (x + 3)
    angle NMO = 5x - 23 - x - 3
    angle NMO = 4x - 26

    angle LMO = angle NMO
    x + 3 = 4x - 26
    3x = 29
    x = 9.67

    check everything, arithmetic, angles, etc

  • Geometry -

    Still a strange question.

    You said above that LMN is a line segment
    so angle LMN = 180°
    so 5x-23 = 180
    x = 40.6°
    then angle LMO=x+3 = 40.6+3 = 43.6
    then angle NMO = 180-43.6 = 136.4°

    So the fact that OM is the bisector of LMN has nothing to do with anything.

  • Geometry -

    My Answer was AngleNMO=45.75 but My teacher says that it is AngleNMO=61..I don't understand how she got this.

  • Geometry -

    Sorry It's Not A Line Segment I Looked At The Wrong Question. LMN is an Angle

  • Geometry -

    The Measure of LMO = x+23.

  • Geometry -

    I got angle NMO = 61
    same method as above, but correction for LMO = x + 32

    Therefore, angle LMO = angle NMO

    angle NMO = angle LMN - angle LMO
    angle NMO = 5x - 23 - (x + 32)
    angle NMO = 5x - 23 - x - 32
    angle NMO = 4x - 55

    angle LMO = angle NMO
    x + 32 = 4x - 55
    3x = 87
    x = 29

    angle NMO = 4x - 55
    x = 29
    4(29) - 55
    116 - 55 = 61

  • Geometry -

    Thank You For Helping Me Understand :)

  • Geometry -

    you're welcome

  • Geometry -

    A preimage includes a line segment of length x and slope m. If the preimage is dilated by a scale factor of n, what are the length and slope of the corresponding line segment in the image

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