Solved Examples: Applying the Exterior Angle Sum to Various Polygons

📚 Quick Study Guide

• 📐 The sum of the exterior angles of any polygon, one at each vertex, is always $360^{\circ}$.
• 🧭 This applies to both regular and irregular polygons.
• 💡 To find the measure of one exterior angle in a regular polygon, divide $360^{\circ}$ by the number of sides ($n$): $\text{Exterior Angle} = \frac{360^{\circ}}{n}$.
• ✏️ An exterior angle is formed by extending one side of the polygon.
• ➕ The exterior angle and its adjacent interior angle are supplementary (they add up to $180^{\circ}$).

Practice Quiz

1. What is the sum of the exterior angles of a hexagon?
   1. $180^{\circ}$
   2. $360^{\circ}$
   3. $540^{\circ}$
   4. $720^{\circ}$
2. What is the measure of one exterior angle of a regular octagon?
   1. $30^{\circ}$
   2. $45^{\circ}$
   3. $60^{\circ}$
   4. $90^{\circ}$
3. If an exterior angle of a regular polygon measures $40^{\circ}$, how many sides does the polygon have?
   1. 6
   2. 7
   3. 8
   4. 9
4. What is the measure of an exterior angle of a regular pentagon?
   1. $60^{\circ}$
   2. $72^{\circ}$
   3. $90^{\circ}$
   4. $108^{\circ}$
5. The measure of an interior angle of a regular polygon is $120^{\circ}$. What is the measure of its exterior angle?
   1. $30^{\circ}$
   2. $60^{\circ}$
   3. $90^{\circ}$
   4. $120^{\circ}$
6. What is the sum of the exterior angles of a triangle?
   1. $90^{\circ}$
   2. $180^{\circ}$
   3. $270^{\circ}$
   4. $360^{\circ}$
7. If a regular polygon has 24 sides, what is the measure of each exterior angle?
   1. $10^{\circ}$
   2. $15^{\circ}$
   3. $20^{\circ}$
   4. $25^{\circ}$