helllllp

∠A   =   180° - 40° - 55°   =   85°

 

Since  ∠A  is the largest angle in triangle BAD, the side opposide ∠A must be the largest side in triangle BAD. That is...

 

BD  >  AB    and

BD  >  AD

 

∠C   =   180° - 75° - 55°   =   50°

 

Since ∠CBD is the largest angle in triangle CBD, the side opposite ∠CBD must be the largest side in triangle CBD. That is...

 

CD  >  BC    and

CD  >  BD

 

So  CD  must be the longest segment.