← Back

6.3 Measures of Each Angle

Ethiopian Grade 9 Mathematics - Unit 6

1. Learning Objectives

2. Key Notes

In a regular polygon, all sides and all angles are equal. We can find individual angle measures by dividing the total sum by the number of sides (n).

Each Exterior Angle = 360° / n

Each Interior Angle = [(n - 2) × 180°] / n

Short-cut: Each Interior Angle = 180° - (Each Exterior Angle)

✍️ Practice Exercises (20 Questions)

Click the button below each question to reveal the explanation.

1. Find each interior angle of a regular pentagon (n=5).
Sum = 540°. Each angle = 540 / 5 = 108°. Ans: 108°
2. Find each exterior angle of a regular hexagon (n=6).
360 / 6 = 60°. Ans: 60°
3. If an interior angle is 144°, how many sides does the polygon have?
Ext angle = 180 - 144 = 36°. n = 360 / 36 = 10. Ans: 10 sides (Decagon)
4. What is each interior angle of a regular octagon (n=8)?
Ext angle = 360 / 8 = 45°. Int angle = 180 - 45 = 135°. Ans: 135°
5. What is the smallest interior angle of a regular polygon?
Found in a triangle (n=3): 180 / 3 = 60°. Ans: 60°
6. Find each exterior angle of a regular decagon (n=10).
360 / 10 = 36°. Ans: 36°
7. Find each interior angle of a square.
360 / 4 = 90°. Ans: 90°
8. If each exterior angle is 30°, find n.
n = 360 / 30 = 12. Ans: 12 sides (Dodecagon)
9. What is each interior angle of a regular dodecagon (n=12)?
Ext angle = 360 / 12 = 30°. Int angle = 180 - 30 = 150°. Ans: 150°
10. If an exterior angle is 72°, what is the interior angle?
180 - 72 = 108°. Ans: 108°
11. A regular polygon has 20 sides. Find its exterior angle.
360 / 20 = 18°. Ans: 18°
12. Find each interior angle of a regular 20-gon.
180 - 18 = 162°. Ans: 162°
13. Can a regular polygon have an interior angle of 100°?
Ext = 180 - 100 = 80°. n = 360/80 = 4.5. n must be a whole number. Ans: No
14. If n = 40, find the exterior angle.
360 / 40 = 9°. Ans: 9°
15. Find each interior angle for n=18.
Ext = 360/18 = 20°. Int = 180 - 20 = 160°. Ans: 160°
16. What happens to the interior angle as n increases?
As n increases, the exterior angle gets smaller, so the interior angle gets larger. Ans: Increases
17. If each interior angle is 60°, name the polygon.
Ext = 180 - 60 = 120°. n = 360 / 120 = 3. Ans: Equilateral Triangle
18. Find n if the interior angle is 170°.
Ext = 180 - 170 = 10°. n = 360 / 10 = 36. Ans: 36 sides
19. Sum of one interior and one exterior angle?
They form a linear pair on a straight line. Ans: 180°
20. Measure of each exterior angle of a heptagon (n=7)?
360 / 7 ≈ 51.4°. Ans: 51.4°