Floor patterns with three polygons at each corner

A designer wants to cover a floor with regular polygon tiles so that at every corner exactly three tiles meet with no gaps: two regular \(n\)-gons and one regular \(m\)-gon.

1. Using the interior angle \(180^\circ-\dfrac{360^\circ}{n}\), show that \(\dfrac4n+\dfrac2m=1\).[2]
2. Find all the pairs of whole numbers \((n,m)\), with \(n,m\ge3\), that satisfy this equation.[3]
3. One solution uses two regular pentagons and a regular decagon at a corner. Explain why this corner cannot be repeated around every corner of a pentagon, so this pattern cannot cover a whole floor.[2]