Interior Angles Exploration

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📐 Part 1: Understanding Angle Sums

1. What is the sum of interior angles in ANY triangle?

90°

180°

270°

360°

2. What is the sum of interior angles in ANY quadrilateral?

180°

270°

360°

450°

3. In a triangle with angles 45°, 60°, and x°, what is the value of x?

Answer: x = _____°

4. In a quadrilateral with angles 85°, 110°, 90°, and y°, what is the value of y?

Answer: y = _____°

🔍 Part 2: Problem Solving

5. A triangle has one angle of 30° and another angle of 75°. Calculate the third angle and show your working.

6. In a rectangle, three angles are each 90°. What is the fourth angle? Explain your reasoning.

7. Challenge Problem: A quadrilateral has angles in the ratio 2:3:4:3. Find each angle.

Hint: Let the angles be 2x, 3x, 4x, and 3x

The four angles are: _____°, _____°, _____°, and _____°

8. Explain in your own words why the sum of interior angles in a triangle is always 180°.

🎯 Part 3: Extension Challenge

9. For Advanced Learners: If a pentagon (5-sided polygon) has interior angles that sum to 540°, can you predict the sum of interior angles for a hexagon (6 sides)?

Show your reasoning:

10. Real-World Application: An architect is designing a triangular roof section. Two of the angles are 55° and 70°. What must the third angle be to ensure the design is structurally sound?

Success Criteria Check: Tick the boxes you can confidently do:

I can explain that triangle interior angles sum to 180°

I can explain that quadrilateral interior angles sum to 360°

I can find unknown angles using angle sum rules

I can use correct mathematical vocabulary