Question

N quadrilateral ABCD, AB produced is perpendicular to DC produced. If A= 44 degree and C= 148 degree, Calculate angle D and angle B.?

Answer 1

the point where AB produced is perpendicular to DC= X
we have right angle ΔAXD and ΔBXC

∠D= ∠A- ∠C
= 90-44
= 46
The exterior angle of a triangle equals the sum of the interior angles
∠B = ∠AXD+ ∠XCB
= 90+(180-148)
= 122

Answer 2

Draw Quadrilateral ABCD and let AB meet DC which was produced at E 

Angle A = 44 Degrees 

Angle C = 148 Degrees 

The triangle produced AED is a right triangle with right angle at E (because AB is perpendicular to DC) 

Angle D = 180- (90+Angle A) 

 = 180-(90+44) 

= 46 Degrees 

 

The sum of angles in a quadrilateral is 360 

Angle B = 360-(Angle A+C+D) 

  = 360-(44+148+46) 

  = 122 Degrees