Answer: 64 degrees
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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
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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
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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
