Answer: 2 (x+5)
Step-by-step explanation:
Answer:
Step-by-step explanation:
<u><em>To Determine:</em></u>
Solve for x and find angle LMN.
<u><em>Fetching Information and Solution Steps:</em></u>
Considering the angle ![\angle{LMN}](https://tex.z-dn.net/?f=%5Cangle%7BLMN%7D)
As MO bisects the angle
into two equal angle parts. These equal angles are:
![\angle{LMO}=6x-22](https://tex.z-dn.net/?f=%5Cangle%7BLMO%7D%3D6x-22)
![\angle{NMO}=2x+34](https://tex.z-dn.net/?f=%5Cangle%7BNMO%7D%3D2x%2B34)
As these angles are equal. i.e.
![\angle{LMO}=\angle{NMO}](https://tex.z-dn.net/?f=%5Cangle%7BLMO%7D%3D%5Cangle%7BNMO%7D)
![6x-22=2x+34](https://tex.z-dn.net/?f=6x-22%3D2x%2B34)
![\mathrm{Add\:}22\mathrm{\:to\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BAdd%5C%3A%7D22%5Cmathrm%7B%5C%3Ato%5C%3Aboth%5C%3Asides%7D)
![6x-22+22=2x+34+22](https://tex.z-dn.net/?f=6x-22%2B22%3D2x%2B34%2B22)
![6x=2x+56](https://tex.z-dn.net/?f=6x%3D2x%2B56)
![\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D2x%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![6x-2x=2x+56-2x](https://tex.z-dn.net/?f=6x-2x%3D2x%2B56-2x)
![4x=56](https://tex.z-dn.net/?f=4x%3D56)
![\mathrm{Divide\:both\:sides\:by\:}4](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D4)
![\frac{4x}{4}=\frac{56}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B4%7D%3D%5Cfrac%7B56%7D%7B4%7D)
![\mathrm{Simplify}](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D)
![x=14](https://tex.z-dn.net/?f=x%3D14)
Hence, ![x=14](https://tex.z-dn.net/?f=x%3D14)
As
was cut into two equal parts
and ![\angle{NMO}](https://tex.z-dn.net/?f=%5Cangle%7BNMO%7D)
So,
= ![\angle{LMO} + \angle{NMO}](https://tex.z-dn.net/?f=%5Cangle%7BLMO%7D%20%2B%20%5Cangle%7BNMO%7D)
= ![6x-22+2x+34](https://tex.z-dn.net/?f=6x-22%2B2x%2B34)
= ![8x + 12](https://tex.z-dn.net/?f=8x%20%2B%2012)
=
∵ ![x=14](https://tex.z-dn.net/?f=x%3D14)
= ![124\textdegree](https://tex.z-dn.net/?f=124%5Ctextdegree)
Therefore, ![\angle{LMN}=124\textdegree](https://tex.z-dn.net/?f=%5Cangle%7BLMN%7D%3D124%5Ctextdegree)
Keywords: angle bisector, congruent angles
Learn more about angle bisector and congruent angles from brainly.com/question/711370
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Answer:
Yes I think so
Step-by-step explanation:
i think an estimate for the answer would be around 90 degrees
Given:
The graphed point is (60,-20).
To find:
The ordered pair that would form a proportional relationship with the given point.
Solution:
If y is proportional to x, then
![y\propto x](https://tex.z-dn.net/?f=y%5Cpropto%20x)
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
![\dfrac{y}{x}=k](https://tex.z-dn.net/?f=%5Cdfrac%7By%7D%7Bx%7D%3Dk)
Where, k is the constant of proportionality.
For the given point,
![k=\dfrac{-20}{60}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B-20%7D%7B60%7D)
![k=\dfrac{-1}{3}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B-1%7D%7B3%7D)
For option (A),
![k=\dfrac{30}{-10}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B30%7D%7B-10%7D)
![k=-3\neq \dfrac{-1}{3}](https://tex.z-dn.net/?f=k%3D-3%5Cneq%20%5Cdfrac%7B-1%7D%7B3%7D)
For option (B),
![k=\dfrac{-15}{30}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B-15%7D%7B30%7D)
![k=-\dfrac{1}{2}\neq \dfrac{-1}{3}](https://tex.z-dn.net/?f=k%3D-%5Cdfrac%7B1%7D%7B2%7D%5Cneq%20%5Cdfrac%7B-1%7D%7B3%7D)
For option (C),
![k=\dfrac{10}{-30}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B10%7D%7B-30%7D)
.
The point (-30,10) gives the same value of the constant of proportionality. So, the point (-30,10) forms a proportional relationship with the given point.
Therefore, the correct option is C.