(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.