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

#### Solution

\[\text{ The sides of the quadrilateral ABCD are produced in order (according to figure) . } \]

\[\text{ Now, we need to find the sum of the exterior angles } . \]

\[\text{ Since the angles made on the same side of straight line are } 180 °, \text{ i . e . , linear pair, we have: } \]

\[a + x + b + y + c + z + w + d = 180° + 180° + 180° + 180°= 720° \]

\[OR \]

\[\text{ Sum of the interior angles + sum of exterior the angles } = 180 ° \times 4 = 720° \]

\[ \text{ Since the sum of the interior angles of a quadrilateral is } 360° , \text{ we have } : \]

\[w + x + y + z = 360° \]

\[ \text{ Substituing the value, we get } : \]

\[a + b + c + d = 360° \]

\[ \therefore \text{ Sum of the exterior angles } = 360 ° \]