Question

Given AB||CD and AD||BC, what is the value of x? ​

Answer 1

Step-by-step explanation:

Angle DOA= Angle EOB (vertically opposite angles)

Angle DOA= 40°

In triangle DAO,

Angle ADO+Angle DAO+ Angle DOA= 180°(Angle sum property)

=) 90°+Angle DAO+ 40°= 180°

=) Angle DAO+90°+40° =180°

=) Angle DAO+130° = 180°

=) Angle DAO= 180°-130°

=) Angle DAO= 50°

In ABCD,

Angle DCB= Angle DAO (opposite angles of a parallelogram are equal)

Angle DCB= 50°

Now,

Angle DCB+ Angle DCH= 180° (linear pair)

=)50°+x= 180°

=) x = 180°-50°

=) x = 130°