Question

given AB||CD. find the value of 'x' and 'm' angle POQ​

Answer 1

Draw a line MN passing through O and parallel to line AB

Now, 

AB∥CD (given) ..............   (1)

AB∥MN (drawn) ..............   (2)

From (1) and (2),

MN∥CD

Now,

AB∥MN

So,

x+u=180∘ .......... (3)         (same-side interior angles)

also,

MN∥CD

so,

y+v=180∘ ........... (4)

Add (3) and (4),

x+y+u+v=360∘

(x+y)+u+v=360∘

∠POQ+∠BPO+∠DQO=360∘

Answer 2

Answer:

x= 30 ; m= 100

Step-by-step explanation:

construct line ST || AB; ST || CD

angle BPO = angle SOP =40 ( alternate interior angle )

angle DQO = angle SOQ = 60 ( alternate interior angle)

therefore , angle POQ = 40+60 =100

3x +10 =100

3x= 90

x=90/3

x= 30