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Polygon Angles Worksheet

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Polygon Angles Worksheet

Various polygons with angle markings

🔍 Part 1: Polygon Identification and Basic Angles

1. Which of these statements about polygons is correct?

A regular polygon has all sides equal but angles can be different

A regular polygon has all sides and all angles equal

An irregular polygon cannot have any equal sides

2. The sum of exterior angles in ANY polygon is always:

180°

360°

It depends on the number of sides

3. A pentagon has _______ sides and a hexagon has _______ sides.

Pentagon: _________ sides Hexagon: _________ sides

4. Complete the formula for finding the sum of interior angles:

Sum of interior angles = (n - _____) × _____°

Where n = number of sides

📐 Part 2: Calculating Interior Angles

5. Calculate the sum of interior angles for a heptagon (7 sides).

Step 1: Write the formula: ________________________

Step 2: Substitute n = 7: ________________________

Step 3: Calculate: ________________________

6. A regular octagon has 8 equal sides and 8 equal angles.

a) Sum of interior angles = ________________°

b) Each interior angle = ________________°

7. In a regular polygon, each interior angle is 120°. How many sides does it have?

Hint: Work backwards using the formula!

🧩 Part 3: Problem Solving with Irregular Polygons

8. An irregular quadrilateral has angles of 85°, 110°, and 95°. Find the fourth angle.

Remember: Sum of angles in quadrilateral = 360°

9. In an irregular pentagon, four angles are: 108°, 98°, 125°, and 115°. Calculate the fifth angle.
10. Psychology Connection: A pie chart showing research data has 5 equal sectors. What is the angle of each sector?

This relates to how psychologists present data in circular graphs.

11. Extension Challenge: Explain why the exterior angles of any polygon always sum to 360°. Use your own words.

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