[tex]m \angle LKN + m \angle \boxed{KLM} = \boxed{180}[/tex] because they are [tex]\text{supplementary angles}[/tex]
This is true of any parallelogram. The adjacent angles of any parallelogram are supplementary, meaning they add to 180 degrees. You can use the same side interior angle theorem here as well.
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Because KA cuts angle K in half, and LA does the same to angle L, this means that we're dividing everything by 2 in that equation at the top of the page. So we have,
[tex]\frac{m \angle LKN + m \angle KLM}{2} = \frac{180}{2}[/tex]
and that turns into
[tex]m \angle LKA + m\angle KLA = 90[/tex]
which tells us that angle KAL must be 90 so that the three angles of triangle KAL add to 180 degrees. For any right triangle, the acute angles are complementary, meaning they add to 90 degrees.
