Answer and Step-by-step explanation:
We can see that because Line K is acting as an Angle Bisector (a line that divides an angle into two angles of equal measures) on angle ∠LMJ, the angles ∠LMK and ∠JMK are equal to each other.
This allows us to solve for angle ∠LMK.
We do this by first setting the angles equal to each other.
10x - 22 = 2x + 66
Now, we want to isolate x by itself. We will subtract 2x from both sides of the equation, and then add 22 to both sides of the equation.
10x - 22 - 2x = 2x + 66 - 2x
8x - 22 = 66
8x - 22 + 22 = 66 + 22
8x = 88
Finally, we will divide both sides of the equation by 8.
8x ÷ 8 = 88 ÷ 8
x = 11
We aren't finished yet, as the question asks to find ∠LMK.
Plug 11 in for x into the equation 10x - 22.
10(11) - 22 =
110 - 22 =
= 88°
So, the measure of angle ∠LMK is 88°.
Have a good day!