the diagonals AC and BD of a rectangle ABCD intersect each other at P. if angle ABD = 50 degree, then angle DPC =
Given: Angle ABD = Angle ABP = 500
Angle PBC + Angle ABP = 900 (Each angle of a rectangle is a right angle)
Angle PBC = 400
Now, PB = PC (Diagonals of a rectangle are equal and bisect each other)
Angle BCP = 400 (Equal sides has equal angles)
In triangle BPC,
Angle BPC + Angle PBC + Angle BCP = 1800 (Angle sum property of a triangle)
Angle BPC = 1000
Angle BPC + Angle DPC = 1800 (Angles in a straight line)
Angle DPC = 1800 - 1000 = 800.
first prove that abcd is a llgm. by the prop. that 2 pairs of opp. sides are equal then its a llgm.
now we know that the diadonals of a llgm. bisect each other.
hence DPA+BPA=180 linear pair
DPA+DPA=180 since Dp=Bp
Bpa = 90
now in triangle apb and dpc
BPA=DPC vert. opp. angles