The sides of a quadrilateral are produced in order.
Question:

The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?

Solution:

The sides of the quadrilateral $\mathrm{ABCD}$ are produced in order (according to figure).

Now, we need to find the sum of the exterior angles.

Since the angles made on the same side of straight line are $180^{\circ}$, i.e., linear pair, we have:

$\mathrm{a}+\mathrm{x}+\mathrm{b}+\mathrm{y}+\mathrm{c}+\mathrm{z}+\mathrm{w}+\mathrm{d}=180^{\circ}+180^{\circ}+180^{\circ}+180^{\circ}=720^{\circ}$

OR

Sum of the interior angles $+$ sum of exterior the angles $=180^{\circ} \times 4=720^{\circ}$

Since the sum of the interior angles of a quadrilateral is $360^{\circ}$, we have:

$w+x+y+z=360^{\circ}$

Substituing the value, we get:

$a+b+c+d=360^{\circ}$

$\therefore$ Sum of the exterior angles $=360^{\circ}$