Opposite angles are equivalent. Therefore,
[tex]5x + 2 = 3(x + 14) \\ 5x + 2 = 3x + 42 \\ 2x = 40 \\ x = 20[/tex]
First, we set the angles equal to each other. Then, we simplify the sides. Then, we subtract 3x from both sides and subtract 2 from both sides. The we divide both sides by 2. Now we know that x = 20, but we're not done yet.
Now we have to find the measure of the angle KNL. We do this by plugging in x:
[tex]3(x + 14) \\ 3x + 42 \\ 3(20) + 42 \\ 60 + 42 \\ = 102[/tex]
First, we simplify. Then, we plug in 20 for x. Then we simplify to find the angle is 102°.
We can check this by looking at the opposite angle:
[tex]5x + 2 \\ 5(20) + 2 \\ 100 + 2 \\ = 102[/tex]
These angles are the same, as they should be.
