Find the measure of angle klm. this is an explain your thoughts question which means you need to: 1) include the properties, theorems, etc. that you used to set up an equation. 2) show the euqation you used to solve for x and thus solve for the angle measure of klm

64 degrees




We'll use these properties:

Property 1: Linear pairs of angles are adjacent (touching) and supplementary. They form a straight angle. By definition they are supplementary meaning they add to 180 degrees.

Property 2: For any triangle, the three angles always add to 180 degrees



We need the measure of angle KLJ in terms of x. 

Notice how KLJ and KLM form the straight angle JLM (which is 180 degrees). So we'll use property 1 mentioned above. Let's isolate angle KLJ to get...

(angle KLM) + (angle KLJ) = 180
(20x+4) + (angle KLJ) = 180 ... use the substitution property to replace angle KLM with its algebraic expression
angle KLJ = 180 - (20x+4)
angle KLJ = 180 - 20x-4
angle KLJ = -20x + 176



Now that we know angle KLJ, we can use this angle along with the angles JKL and KJL. Basically we're focusing on the smaller triangle on the left (the obtuse triangle)

Add those three angles up and set the result equal to 180 degrees. I'm using property 2 now. 

(angle KLJ) + (angle KJL) + (angle JKL) = 180
(-20x+176) + (6x+4) + (8x+18) = 180

Therefore the equation we need to solve is: (-20x+176) + (6x+4) + (8x+18) = 180

Let's do so...
(-20x+176) + (6x+4) + (8x+18) = 180
-20x+176 + 6x+4 + 8x+18 = 180
(-20x+6x+8x)+(176+4+18) = 180
-6x+198 = 180
-6x+198-198 = 180-198
-6x = -18
-6x/(-6) = -18/(-6)
x = 3

After solving for x, we get x = 3
Let's use this to find the measure of angle KLM

angle KLM = 20*x+4
angle KLM = 20*3+4
angle KLM = 60+4
angle KLM = 64