Question

Find x and the measure of LKM if m4JKL = x + 2, m LKM = 2x - 8, and mZJKM = 102.

X = ?
Measure of LKM = ?

Answer 1

To find x, we set up and solved the equation (x + 2) + (2x - 8) = 102, yielding x = 36. To find the measure of angle LKM, we used the equation m LKM = 2x - 8 and found it to be 64 degrees.

Step-by-step explanation:

To find the value of x, we will use the information given for the measures of angles JKL and LKM, and the overall angle JKLM. We have the equations m4JKL = x + 2 and m LKM = 2x - 8. We also have that mZJKM = 102. Since JKLM is a straight line, the measures of angles JKL and LKM should add up to the measure of angle JKLM.

We set up the equation: (x + 2) + (2x - 8) = 102. Simplifying this equation, we get 3x - 6 = 102. Adding 6 to both sides, we get 3x = 108. Dividing both sides by 3, we find that x = 36.

Now we can find the measure of LKM. Plugging x into the second equation we get: 2 * 36 - 8 = 72 - 8 = 64. Therefore, the measure of LKM is 64 degrees.