Angles Irregular Polygons Demonstration This resource provides animated

Angles – Irregular Polygons – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

Polygon Greek: Poly- "many“, -gon "angle" Regular = sides/angles all equal Regular Hexagon 2. 1. 5. 6. Which of these shapes are polygons? Which are regular? Which are irregular? Can you name them? Irregular Hexagon 3. Regular Decagon 4. Irregular Octagon 7. Irregular Hexagon 8. 11. 10. Regular Octagon 12. 9. Regular Pentagon Regular Triangle

Polygon Greek: Poly- "many“, -gon "angle" Regular = sides/angles all equal Exterior Angle Hexagon Interior Angle Irregular Hexagon Pentagon How can we calculate interior and exterior angles of polygons?

We know the interior angles of a triangle total 180°. 60° 50° How can we work out the interior angles of a quadrilateral? 70° If we divide it into 2 triangles, we can see the interior angles must total 360°.

How can we work out the total interior angles of a pentagon? 180° If we split the shape into three triangles, We can see the total of the interior angles must be: 3 × 180° = 540°

We can see that any polygon can be divided into triangles. The amount of triangles is two less than the number of sides (n). Regular Pentagon Irregular Octagon Total Interior Angles = 3 × 180° = 540° Total Interior Angles = 6 × 180° = 1080° The formula for any regular or irregular polygon is: Sum of Interior Angles = (n− 2) × 180

DEMO Finding Angles in Irregular Polygons 75° 80° (4− 2) × 180 = 360° Interior Angles of a Quadrilateral Total 360° 360 − 80 − 90 − 75 = 115° Sum of Interior Angles = (n− 2) × 180

DEMO Finding Angles in Irregular Polygons 135° 95° 100° 110° 125° (6− 2) × 180 = 720° Interior Angles of a Hexagon Total 720° 720 − 95 − 110 − 125 − 100 − 135 = 155° Sum of Interior Angles = (n− 2) × 180

DEMO YOUR TURN Finding Angles in Irregular Polygons 135° 95° 100° 130° 110° 125° 120° 125° (6− 2) × 180 = 720° Interior Angles of a Hexagon Total 720° (5− 2) × 180 = 540° Interior Angles of a Pentagon Total 540° 720 − 95 − 110 − 125 − 100 − 135 = 155° 540 − 130 − 90 − 125 − 120 = 75° Sum of Interior Angles = (n− 2) × 180

DEMO YOUR TURN Finding Angles in Irregular Polygons 135° 100° 95° 130° 160° 150° 110° 125° (6− 2) × 180 = 720° Interior Angles of a Hexagon Total 720° 720 − 95 − 110 − 125 − 100 − 135 = 155° Sum of Interior Angles = (n− 2) × 180 120° 150° 110° (8− 2) × 180 = 1080° Interior Angles of an Octagon Total 1080° 1080 − 110 − 150 − 130 − 160 − 120 − 110 − 150 = 150°

DEMO YOUR TURN Finding Angles in Irregular Polygons 135° 100° 95° 100° 110° 125° (6− 2) × 180 = 720° Interior Angles of a Hexagon Total 720° 720 − 95 − 110 − 125 − 100 − 135 = 155° Sum of Interior Angles = (n− 2) × 180 95° 135° 175° (7− 2) × 180 = 900° Interior Angles of an Heptagon Total 720° 900 − 90 − 175 − 135 − 95 − 100 = 215° Concave Heptagon (1+ diagonals are outside the shape)

DEMO YOUR TURN Finding Angles in Irregular Polygons 135° 95° 100° 110° 125° (6− 2) × 180 = 720° Interior Angles of a Hexagon Total 720° 720 − 95 − 110 − 125 − 100 − 135 = 155° Sum of Interior Angles = (n− 2) × 180 (5− 2) × 180 = 540° Interior Angles of an Pentagon Total 540° 540 − 460 = 80°

DEMO YOUR TURN Finding Angles in Irregular Polygons 135° 95° 100° 110° 125° (6− 2) × 180 = 720° Interior Angles of a Hexagon Total 720° 720 − 95 − 110 − 125 − 100 − 135 = 155° Sum of Interior Angles = (n− 2) × 180 (10− 2) × 180 = 1440° Interior Angles of an Decagon Total 1440° 1440 − 1305 = 135°

Sum of Interior Angles = (n− 2) × 180 1) Find the sum of the interior angles of… 540° …a pentagon. …a nonagon. …a heptagon. 1260° 900° 1800° ÷ 12 = 150° 135° 115° 105° 540° − 345° = 90° 5) A pentagon has interior angles in the ratio 2 : 3 : 4 : 9 Find the size of the smallest interior angle. 95° 540° ÷ 20 = 27° 720° − 565° = 155° 75° 135° 45° 130° 135° 6) An irregular octagon has equal interior angles, except one that is 40° larger than the others. What is the size of this angle? 130° + 40° = 170°

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk