Draw an MKN angle of 140 degrees. With the KP beam, divide this angle into two angles so that the PKN

Draw an MKN angle of 140 degrees. With the KP beam, divide this angle into two angles so that the PKN angle is 55 degrees. Calculate the angle measure MKP.

The KP beam emanates from the vertex K of the MKN angle and divides it into two parts, so the MKN angle is equal to the sum of the PKM and PKN angles:
∠MKN = ∠PKN + ∠PKM, hence we get:
∠PKM = ∠MKN – ∠PKN;
∠PKM = 140 ° – 55 ° = 85 °.