Final answer:
D) 39 degrees Thus, 180 degrees - (56 degrees + 135 degrees) = 180 degrees - 191 degrees = 39 degrees, making option D (39 degrees) the correct measure for angle ZP.
Explanation:
To determine the measure of angle ZP, we utilize the property of angles in a triangle. By observing the given figure, ZP is part of a triangle with two known angles: 56 degrees and 135 degrees.
As the sum of angles in a triangle is always 180 degrees, we subtract the sum of the known angles (56 degrees + 135 degrees) from 180 degrees to find the measure of angle ZP. Thus, 180 degrees - (56 degrees + 135 degrees) = 180 degrees - 191 degrees = 39 degrees, making option D (39 degrees) the correct measure for angle ZP.
In the provided triangle, the angle sum property is crucial in solving for the unknown angle. We subtract the sum of the known angles from the total degrees in a triangle to isolate the measure of angle ZP accurately. This mathematical concept helps determine the value of an unknown angle within a geometric shape based on the established properties of angles within triangles.