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Angles in Polygons Worksheet

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Angles in Polygons Worksheet

Geometric polygons with angles

🎯 WALT: We Are Learning To calculate angles in polygons

Success Criteria:

• I can identify interior and exterior angles

• I can calculate missing angles using polygon formulae

• I can apply angle properties to solve problems

Key Formulae:

• Sum of interior angles = (n - 2) × 180°

• Each interior angle in regular polygon = (n - 2) × 180° ÷ n

• Sum of exterior angles = 360°

📚 Part 1: Multiple Choice Questions

1. What is the sum of interior angles in a pentagon?

360°

540°

720°

900°

2. Each interior angle of a regular hexagon measures:

108°

120°

135°

140°

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

180°

360°

540°

It depends on the number of sides

4. Which of these are properties of regular polygons? (Tick all that apply)

All sides are equal

All angles are equal

All exterior angles are equal

The polygon must have 6 sides

✏️ Part 2: Calculations and Problem Solving

5. Calculate the sum of interior angles in an octagon (8 sides).

Formula: Sum = (n - 2) × 180°

Answer: ____________°

6. In a regular decagon (10 sides), calculate each interior angle.

Step 1: Find sum of all interior angles: ____________°

Step 2: Divide by number of angles: ____________°

7. The interior angles of a quadrilateral are 85°, 110°, 95° and x°. Find x.

Remember: Sum of interior angles in quadrilateral = 360°

x = ____________°

8. Challenge Question: If each exterior angle of a regular polygon is 24°, how many sides does it have?

Hint: Sum of exterior angles = 360°

Number of sides = ____________

9. Explain in your own words why the sum of exterior angles is always 360°.

🌟 Extension Activities

For Advanced Learners:

• Research the relationship between interior and exterior angles

• Investigate angle properties in star polygons

• Create your own polygon angle problems

Dyslexia-Friendly Support:

• Use coloured pens to highlight key information

• Break complex problems into smaller steps

• Draw diagrams to visualise the polygons

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