Begin by removing the shingles down to the wood sheathing and slip a strip of adhesive ice and water barrier available where roofing repair products are sold under the soffit main roof joint.
Roof joint leak addition.
Check plumbing vent boots and roof vents if water is entering from that area to cause the leaking roof.
Loose gutters gutters that were improperly installed or gutters filled with debris may cause water to back up into the roof and leak through an exterior overhang.
Look for cracks in the base of flexible rubber flashing or broken seams in metal varieties of vent pipe flashing.
Melting ice that drips onto a home addition also complicates the matter when you have a leak.
Leak where addition meets house had similar situation as todd second roof on top of original on old section the flashing was under first layer of old roof.
Another technique for avoiding leaks involves laying rows of shingles over tar paper to prevent damage to the sheathing.
2plumbing vent boots and roof vents.
When it would rain the water would run down chimney and dormers under second layer and dump into old gutters.
The rubber gasket that surrounds the vent pipe could be rotted.
In the case of a lean to roof over an addition the existing rafters will have to be cut away to accommodate the addition and the shed roof will require support where.
A well ventilated attic should help prevent leaks on your roof in the winter.
Attaching below the ridge.