The unfolded angle NPK is divided by the beam PR into two angles NPR and RPK.

The unfolded angle NPK is divided by the beam PR into two angles NPR and RPK. Find the degree measures of these angles if the NPR angle is half the RPK angle.

Let the degree measure of the NPR angle be X degrees, then the degree measure of the RPK angle will be 2 ∙ X degrees, since by the condition of the problem it is known that the NPR angle is two times less than the RPK angle. The degree measure of the extended NPK angle is 180 degrees.
Knowing that the unfolded angle NPK is divided by the ray PR into two angles NPR and RPK, we compose the equation:
X + 2 ∙ X = 180 °;
X = 60 ° – degree measure of NPR angle;
2 ∙ X = 120 ° – the degree measure of the RPK angle.
Answer: The degree measure of the NPR angle is 60 °; the degree measure of the RPK angle is 120 °.