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Polygon Angles Worksheet

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Polygon Angles Worksheet worksheet preview

Polygon Angles Worksheet

Polygon angles illustration

📐 Part 1: Multiple Choice Questions

1. What is the formula for finding the sum of interior angles in a polygon with n sides?

(n + 2) × 180°

(n - 2) × 180°

n × 180°

(n - 1) × 180°

2. What is the sum of exterior angles for ANY polygon?

180°

360°

540°

It depends on the number of sides

3. A regular hexagon has how many sides?

5

6

7

8

4. Which of these angle facts are TRUE? (Select all that apply)

Angles on a straight line = 180°

Angles around a point = 360°

Vertically opposite angles are equal

All interior angles in a polygon are equal

✏️ Part 2: Calculations and Problem Solving

5. Calculate the sum of interior angles in a pentagon (5 sides).

Formula: (n - 2) × 180° = (_____ - 2) × 180° = _____ × 180° = _____°

6. A regular octagon has 8 equal sides and 8 equal angles. Calculate ONE interior angle.

Step 1: Sum of interior angles = (8 - 2) × 180° = _____°

Step 2: One interior angle = _____ ÷ 8 = _____°

7. In an irregular quadrilateral, three angles are 85°, 110°, and 95°. Find the fourth angle.

Remember: Sum of interior angles in a quadrilateral = _____°

8. Psychology Application: A pie chart showing different therapy types has 5 equal sections. What angle does each section represent?

Total degrees in a circle = _____° ÷ 5 sections = _____° per section

🧠 Part 3: Extension and Reasoning

9. Extension: If each exterior angle of a regular polygon is 40°, how many sides does it have?

Hint: Sum of exterior angles = 360°, so number of sides = 360° ÷ 40° = _____

10. Reasoning: Explain in your own words why the exterior angles of any polygon always add up to 360°.
11. Challenge: Create your own irregular pentagon with angles 120°, 105°, 98°, and 115°. Calculate the fifth angle and draw your polygon.

Calculation: Fifth angle = _____°

📚 Dyslexia-Friendly Key Terms

Polygon: A shape with straight sides (triangle, square, pentagon, etc.)

Interior angle: An angle INSIDE the polygon

Exterior angle: An angle OUTSIDE the polygon

Regular polygon: All sides and angles are EQUAL

Irregular polygon: Sides and angles are NOT all equal

Formula to remember: Sum of interior angles = (n - 2) × 180°

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