Question

ABCD is a quadrilateral in which AB ll DC and AD ll BC. Find ∠b, ∠c and ∠ d.

Answer 1

Hy there,
Since AB || DC and AD || BC, it is proved that its a parallelogram.
Angle A is 50 degree, so in a parallelogram opposite angles are congruent, implies that angle A=angle C=50 degree.
Also, consecutive angles are supplementary, implies that Angle D+ Angle A=180 degree.
Implies Angle D+50=180.
Implies Angle D=180-50=130.
Since, opposite angles are congruent,
Implies Angle D=Angle B=130.
Conclusion -
A=50
B=130
C=50
D=130
Hope it helps.
Regards.
Thanks.

Answer 2

<A = <C = 50 (OPPOSITE ANGLES ARE EQUAL)

<B = 180-50 (SUM OF ADJACENT ANGLE IS EQUAL TO 180)

= 130

<D = <B = 50 (OPPOSITE ANGLES ARE EQUAL)