Question

In quadrilateral ABCD,AB produced is perpendicular to DC produced.If A=44° and C=148°,calculate D and B.

Answer 1

Let AB extended intersect DC extended at point E 
We now have right triangle BEC with E = 90 degrees 

For triangle BEC: 
Exterior angle at E = 90 
Exterior angle at C = 148 (given) 
Exterior angle of all polygons add up to 360 degrees 
Exterior angle at B = 360−148−90 = 122 

So in quadrilateral ABCD 
B = 122 
D = 360−44−148−122 = 46