Question

In rectangle KLMN, the angle bisector of ???NKM intersects the longer side at point P. The measure of ???KML is equal to 54??. Find the measure of ???KPM

Answer 1

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°

Answer 2

The measure of ∠KPM comes to be 117°.

Find the attached picture to visualize the problem.

Since KP is the angle bisector

So, ∠NKP =∠PKM = 54/2

∠PKM = 27°

It is given that

∠KML = 54°

So, ∠KML = 90-54 = 36°

What is the sum of interior angles of a triangle?

The sum of interior angles of a triangle is 180°.

So, ∠KPM + ∠PKM + ∠KMP = 180°

∠KPM + 27°+ 36° = 180°

∠KPM = 180°-(27°+ 36°) = 117°

Therefore, the measure of ∠KPM comes to be 117°.

To get more about rectangles visit:

https://brainly.com/question/1168982