Line MP bisects <LMN, m<LMP=4x+3 and m<LMN=10x-6. Find m<LMN.
I understand how to find adjacent angles and the complement. I don't understand what I am supposed to do? Since it already give you the answer 10x-6, should I solve for x?
since MP bisects <LMN, m<LMP is 1/2 of m<LMN. So,
m<LMN = 2(m<LMP)
10x-6 = 2(4x+3)
Now find x and m<LMN = 10x-6
Thank you! :)
To find the measure of angle <LMN, we need to use the fact that line MP bisects <LMN, which means that angle <LMP and angle <LMN are congruent.
Given:
m<LMP = 4x + 3
m<LMN = 10x - 6
Since line MP bisects <LMN, we can set up an equation by equating the measures of angle <LMP and angle <LMN:
m<LMP = m<LMN
We can substitute the given values for m<LMP and solve for x:
4x + 3 = 10x - 6
To solve this equation, we need to isolate the variable x.
First, let's get all the x terms on one side by subtracting 4x from both sides:
4x - 4x + 3 = 10x - 4x - 6
This simplifies to:
3 = 6x - 6
Next, let's get rid of the constant term by adding 6 to both sides:
3 + 6 = 6x - 6 + 6
This simplifies to:
9 = 6x
Now, we can isolate x by dividing both sides by 6:
9/6 = 6x/6
This simplifies to:
3/2 = x
Therefore, x = 3/2.
Now that we have the value of x, we can substitute it back into the expression for m<LMN to find the measure of angle <LMN:
m<LMN = 10x - 6
Substituting x = 3/2:
m<LMN = 10(3/2) - 6
This simplifies to:
m<LMN = 15 - 6
Therefore, the measure of angle <LMN is:
m<LMN = 9 degrees