In rectangle klmn, the angle bisector of intersects the longer side at point p. the measure of is equal to find the measure of

See the attached picture to better understand the problem

we know that
∠PML=90°
∠KML=54°
∠KMP+∠KML=90°------------> by complementary angles
so
∠KMP=90-54-----> ∠KMP=36°

∠NKM=∠KML
∠NKM=54°
so
the angle bisector of ∠NKM =∠PKM
∠PKM=∠NKM/2-----> ∠PKM=54/2--------> ∠PKM=27°

we know that
the sum of the internal angles of a triangle is equal 180 degrees

in the triangle PKM
∠PKM+∠KPM+∠KMP=180°
∠KPM=180-[∠PKM+∠KMP]-----> 180-[27+36]----> 117°
∠KPM=117°

the answer is
∠KPM is 117°