In △ABC ∠BAC+∠ABC+∠ACB=180∘ (Angle sum property)∠BAC+69∘+31∘=180∘ ∠BAC=180∘−100∘=80∘ For segment BADCB,V BDC and ∠BAC are angles in the same segment. So, they must be equal ∴∠BDC=∠BAC (Angles in the same segment are equal)∠BDC=80∘