In the figure, if AB∥CD, CD∥EF and y:z=3:7, find x.

Given, AB∥CD and CD∥EF
y:z=3:7
Now, x+y=180° (Angles on the same side of transversal)
Also, Let ∠O=∠Z (Corresponding angles)
and ∠Y+∠O=180° (Linear pair)
⇒y+z=180°
According to the question,
y=3w and z=7w
3w+7w=180°
⇒10w=180°
⇒w=18°
∴y=3×18°=54° and z=7×18°=126°
Now, x+y=180°
⇒x+54°=180°
⇒x=126°