Explore the interior angles of polygons by following these steps.
✓ 1. Press Continue to partition the quadrilateral into triangles.
✓ 2. Because the sum of angle measures in each triangle is 180°, the sum of interior angle measures in a quadrilateral is
2 × 180° =
.
✓ 3. A polygon with 5 sides can be partitioned into how many triangles?
✓ 4. What is the sum of interior angle measures in a polygon with 5 sides?
3 × 180° =
✓ 5. What is the calculation for the sum of interior angle measures in a polygon with 6 sides?
× 180° = 720°
✓ 6. What is the calculation for the sum of interior angle measures in a polygon with 7 sides?
× 180° = 900°
✓ 7. Make a conjecture. What is the formula for the sum of interior angle measures in a polygon with n sides?
× 180°
Number of Sides
Number of Triangles
Sum of Interior Angle Measures
3
1
1 × 180° = 180°
4
2
2 × 180° = 360°
5
3
3 × 180° = 540°
6
4
4 × 180° = 720°
7
5
5 × 180° = 900°
n
n − 2
(n − 2) × 180°