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3.6 – Angles in Polygons

3.6 – Angles in Polygons. Sum of the Interior Angles. We can find the sum of all the angles inside a CONVEX polygon using 2 main methods. The polygon MUST be convex. Sum of the Interior Angles. Sum of the Interior Angles. Triangle Method. 3. 2. 1. 3 triangles (180  each).

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3.6 – Angles in Polygons

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  1. 3.6 – Angles in Polygons

  2. Sum of the Interior Angles • We can find the sum of all the angles inside a CONVEX polygon using 2 main methods. • The polygon MUST be convex.

  3. Sum of the Interior Angles

  4. Sum of the Interior Angles • Triangle Method 3 2 1 3 triangles (180 each) 3(180 ) = 540 If you add up all the angles in this polygon, it would equal 540°

  5. Sum of the Interior Angles • Formula • 180(n – 2) where n is the number of sides of the polygon Number of sides = 5 180(5 – 2) 540 180(3)

  6. Interior Angles Practice

  7. Sum of the Interior Angles • If the polygon is REGULAR you can find the measure of ONE interior angle • Remember that in a regular polygon, all the angles are the same!

  8. Sum of the Interior Angles Is it a regular polygon? ….. YES! Number of sides = 8

  9. One Interior Angle Practice

  10. Exterior Angles of Polygons • The sum of all the exterior angles of any convex polygon is always 360 • If the polygon is regular, you can find the measure of each exterior angle (because they are all congruent)

  11. Exterior Angles of Polygons All the angles (1 to 6) add up to give us 360 1 2 6 Number of sides = 6 3 5 4

  12. Practice

  13. Practice

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