In the given figure, AB || CD. Find the value of x.

Draw a line EF through point M such that EF is parallel to both AB and CD.

From the figure,

∠PAB = 3x°, ∠OCD = 2x° and ∠PMO = 100°

For AB || ME:

∠AME = ∠PAB $\quad$[Corresponding angles]

∴ ∠AME = 3x° $\quad$[Substituting the value of ∠PAB]

For CD || ME:

∠CME = ∠OCD $\quad$[Corresponding angles]

∴ ∠CME = 2x° $\quad$[Substituting the value of ∠OCD]

As the line ME splits the 100° angle at point M into two parts:

∴ ∠AME + ∠CME = 100°

⇒ 3x° + 2x° = 100°

⇒ 5x° = 100°

⇒ x° = $\dfrac{100^{\circ}}{5}$

x° = 20°