Question

please help me find measure of angle LKM if measure of LKN = 145°

Answer 1

We have to find angle LKM and we know that the measure of the angle LKN is 145°.

Angle LKN is represented in red in the following image:

As we can see, the angle of 145° is the result of adding the angle 2x+10 and the angle 4x-3. So to find the value of x (and then the value of LKM) we can use the following equation:

$2x+10+4x-3=145$

To solve this equation for x, we add the like terms on the right side of the equation. First, we add 2x and 4x which is 6x:

$6x+10-3=145$

Then we combine the terms 10 and -3 and we get +7:

$6x+7=145$

Next, subtract 7 to both sides of the equation:

$\begin{gathered} 6x=145-7 \\ 6x=138 \end{gathered}$

Finally, to solve for x, divide both sides by 6:

$\begin{gathered} \frac{6x}{6}=\frac{138}{6} \\ x=23 \end{gathered}$

Now that we have the value of x, we can find the value of the angle LKM:

$\text{LKM}=2x+10$

Substituting x=23:

$\text{LKM}=2(23)+10$

Solving the operations:

$\begin{gathered} \text{LKM}=46+10 \\ \text{LKM}=56 \end{gathered}$

Answer: 56°