Interior Angles Exploration

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📐 Part 1: Understanding Interior Angles

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°

540°

3. In a triangle with angles 45° and 85°, what is the third angle?

Answer: _______°

4. A quadrilateral has angles of 90°, 110°, and 75°. Find the fourth angle.

Answer: _______°

🔍 Part 2: Problem Solving

5. In triangle ABC, angle A = 2x°, angle B = 3x°, and angle C = x°. Find the value of x.

x = _______°

Therefore: Angle A = _______°, Angle B = _______°, Angle C = _______°

6. A rectangle has one corner "cut off" to form a pentagon. If four of the interior angles are 90°, 90°, 90°, and 135°, what is the fifth angle?

Fifth angle = _______°

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

🌟 Part 3: Extension Challenge

8. Advanced: A regular pentagon (5 equal sides) has all interior angles equal. Calculate the measure of each interior angle.

Hint: The sum of interior angles in a pentagon is (5-2) × 180° = 540°

Each interior angle = _______°

9. Investigation: Draw any triangle and extend one side. Measure the exterior angle formed. How does it relate to the two non-adjacent interior angles? Record your findings.

10. Real-world Application: An architect is designing a triangular garden bed. Two angles of the triangle are 65° and 40°. What should the third angle be to complete the design?

Third angle = _______°