A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The measure of ∠KPM is 119°.
What is a rectangle?
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
The diagram for the given rectangle can be made as shown below.
Since all the angles of a rectangle are of 90° measurement. Therefore, the measure of the ∠MKP can be written as,
∠MKP = ∠NKL - ∠NKM
∠MKP = 90° - 58°
∠MKP = 32°
The opposite sides of the rectangle are parallel and equal, therefore, we can write,
∠NKM = ∠KML = 58° {Alternate interior angles}
Given that the MP is the angle bisector of ∠KML, therefore,
∠KMP = ∠PML
∠KML = ∠KMP + ∠PML
∠KML = 2∠KMP
∠KMP = 29°
In ΔKPM, the sum of all the angles can be written as,
∠MKP + ∠KMP + ∠KPM = 180°
32° + 29° + ∠KPM = 180°
∠KPM = 119°
Hence, the measure of ∠KPM is 119°.
Learn more about Rectangle:
https://brainly.com/question/15019502
#SPJ2
