(1) Because MB and NB are angular bisectors, so
The angle mbn = MBC+NBC =1/2 (ABC+PBC) =1/2×180 = 90 degrees.
Same angle MCN=90 degrees
Then in the quadrilateral NBMC, angle M+ angle N=360-90-90= 180 degrees.
(2) The degree of angle M+ angle n will not change, because no matter how B and C change and move, NB, NC, MB and MC are bisectors of angles, and angles MBN and NCM are half of right-angle ABP and ACQ, so angle M+ angle N= 180 remains unchanged!
(3) The same is true.
Come on, Shan.