Foundation and Higher · angles in polygons
Any polygon.
Split it into
triangles.
each triangle
is 180°
a shape with straight sides —
Polygon
interior angles are inside
exterior angles turn the corner
step 1 of 4
Split into triangles
1. Draw diagonals from one corner.
2. Always 2 fewer triangles than sides.
✓ A pentagon adds to 540°
5 sides → 3 triangles
3 × 180° = 540°
step 2 of 4
The formula
1. n is the number of sides.
2. A hexagon: 6 sides, so 4 triangles.
✓ Interior angles add to 720°
sum = (n − 2) × 180°
(6 − 2) × 180° = 720°
step 3 of 4
Regular: equal angles
1. Regular means every angle is the same.
2. Share the total between the 6 corners.
✓ 120° each
720° ÷ 6
each interior angle = 120°
step 4 of 4
Exterior angles: 360°
1. Exterior angles always add to 360°.
2. Interior + exterior = 180°.
✓ Often the quicker way in
360° ÷ 6 = 60°
interior = 180° − 60° = 120°
angles in polygons —
Regular
divide the sum by n
Exterior
always add to 360°
Given an exterior angle?
360 ÷ it = number of sides.
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