Question

In quadrilateral ABCD angleA = 80° and angleB =84°.the bisector of angle C and angle D meet at point P.find the angle CPD.

Answer 1

In Δ AMB, angles AMB+BAM+MBA = 180  i.e., AMB +À/2 +B/2 =180  So, Angle AMB = 180 -(A/2+B/2)……………(1)  A+B+C+D =360 (sum of the angles of a quadrilateral)  So A/2 +B/2 + C/2 +D/2 =180  1/2(C/2 + D/2) = 180 -(A/2 +B/2) ……..(2)  From (1) and (2), Angle AMB = 1/2(C/2 + D/2)