Let’s write the value of x in each of the following figure.

The given figure is as shown below:

Given ∠ABC = 40°, ∠BAD = 60°, ∠ADC = 20°

To find the exterior angle, i.e., ext ∠BCD = x°

Now the given figure is a concave quadrilateral; we will divide it into two by drawing a line joining AC.

By doing this we will get two triangles,

⇒ Quadrilateral ABCD = ΔABC + ΔADC

We know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

⇒ Quadrilateral ABCD = 180° + 180° = 360°

So in a quadrilateral the sum of all four interior angles is equal to 360°.

So in the given quadrilateral,

∠ABC + ∠BCD + ∠ADC + ∠BAD = 360°

Substituting the values, we get

40° + ∠BCD + 20° + 60° = 360°

⇒ ∠BCD = 360° - 60° - 20° - 40°

⇒ int. ∠BCD = 240°

From figure ∠BCD is reflex angle, so

360° = interior ∠BCD + Exterior ∠BCD

⇒Ext ∠ BCD = 360° - int. ∠BCD

Substituting the values, we get

⇒Ext ∠ BCD = 360° - 240°

⇒Ext ∠ BCD = 120°

So the measurement of exterior angle in the given figure is 120°.