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Polygon Interior Angles

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Polygon Interior Angles

Polygon Interior Angles

Various polygons with interior angles marked

📐 Part 1: Interior Angle Formula Knowledge

1. What is the formula for finding the sum of interior angles in a polygon?
2. Calculate the sum of interior angles for each polygon:

a) Triangle: ________________°

b) Quadrilateral: ________________°

c) Pentagon: ________________°

d) Hexagon: ________________°

e) Octagon: ________________°

3. If a regular polygon has 12 sides, what is the measure of each interior angle?

📏 Part 2: Measuring Interior Angles

4. Draw a quadrilateral (4-sided polygon) in the space below. Use your protractor to measure each interior angle and record the measurements.

Angle 1: ______° Angle 2: ______° Angle 3: ______° Angle 4: ______°

Sum of measured angles: ________________°

Expected sum using formula: ________________°

5. Draw an irregular pentagon (5-sided polygon) and measure all interior angles:

Angle 1: ______° Angle 2: ______° Angle 3: ______°

Angle 4: ______° Angle 5: ______°

Sum of measured angles: ________________°

Expected sum using formula: ________________°

🧮 Part 3: Finding Missing Angles

6. In a quadrilateral, three angles measure 85°, 92°, and 108°. What is the measure of the fourth angle?
7. A regular hexagon has all angles equal. Calculate the measure of each interior angle.
8. In a pentagon, four angles measure 95°, 110°, 125°, and 88°. Find the fifth angle.

🤔 Part 4: Analysis and Reasoning

9. True or False? Circle your answers:

a) The sum of interior angles in any triangle is always 180°

True
False

b) A regular polygon has all sides and angles equal

True
False

c) The more sides a polygon has, the larger the sum of interior angles

True
False

10. Why might your measured angles not exactly equal the calculated sum? List at least two reasons:
11. Explain the relationship between the number of sides in a polygon and the sum of its interior angles:

🎯 Part 5: Challenge Problems

12. Design your own irregular polygon with 6 sides. Calculate what the sum of interior angles should be, then measure to verify:

Calculated sum: ________________°

Measured sum: ________________°

Difference: ________________°

13. If each interior angle of a regular polygon measures 140°, how many sides does the polygon have?
14. Reflection: How can understanding interior angles of polygons be useful in real life? Give at least one example:

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