To solve this problem, we should follow these steps:
1. Angle XYP and Angle MPF are supplementary because they are angles on a straight line. We can calculate the measure of Angle XMP as it is the difference between Angle XYP and Angle XYP, which is 440° - 90°. The computation gives us 350°.
2. The next step involves Angle XMP and Angle MFP. These two are also supplementary. Subtract the shared angle (90°) from the total Angle MPF (460°) to get Angle XMF. We proceed with the calculation 460° - 90° and obtain an angle of 370°.
3. Since we have been told triangle XYM is isosceles (meaning that Angle XYP and Angle MYP are equal), |XY| is equal to |XM|. This gives us that |XM| equals 7cm.
4. Finally, we need to find |MF| (which we can equate to |YF| because MFP is an isosceles triangle). To do this, we behave like the triangle MFP, using the Law of Sines.
We first need to find Angle FMP. It could be calculated as the difference of 180° minus Angle XMF and Angle XYP, i.e., 180° - 370° - 90°.
With the Angle FMP, we can now apply the Sine rule:
|MF| = MP * (sin Angle XMF / sin Angle FMP)
This computes to |YF| equals approximately 1.587cm, which we can round off to 1.59cm.
In conclusion, XM equals 7cm, YF approximately equals 1.59cm, and Angle XMP equals 350°.