In your journal, create this chart PolygonNumber of Angles Sum of degrees Place your tan homework on your desk.

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Presentation transcript:

In your journal, create this chart PolygonNumber of Angles Sum of degrees Place your tan homework on your desk

Expectations Explain how the formula for the sum of angles of a polygon is derived Compute problems regarding the sum of angles of a polygon

How many degrees in the sum of the interior angles of a triangle? 180 Degrees

Add the data to the chart PolygonNumber of Angles Sum of degrees Triangle3180

How many degrees in the sum of the interior angles of a quadrilateral? 360 Degrees

Add the data to the chart PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360

How many degrees in the sum of the interior angles of a pentagon? = 540

Add the data to the chart PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360 Pentagon5540

Add the data to the chart PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6710

Add the data to the chart PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6710 Heptagon7890

Look for a pattern PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6710 Heptagon The sum of the degrees increases 180 degrees for every additional angle

Look for a pattern PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6710 Heptagon7890 What is the relationship between the number multiplied by 180 and number of sides of a triangle? 2 x 180 = 3 x 180 = 4 x 180 = 5 x 180 = 1 x 180 =

Look for a pattern PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6710 Heptagon7890 What is the relationship between the number multiplied by 180 and number of sides of a triangle? 2 x 180 = 3 x 180 = 4 x 180 = 5 x 180 = 1 x 180 = or Number of angles – 2 times 180 = sum of degrees (n-2)180 = Sum of degrees

What is the sum of all the angles of an octagon? (n-2)180 = Sum of degrees (8-2)180 = Sum of degrees (8-2)180 = Sum of degrees 6 x 180 = 1080

What is the sum of all the angles of an nonagon? (n-2)180 = Sum of degrees (9-2)180 = Sum of degrees (9-2)180 = Sum of degrees 7 x 180 = 1260

Record formula in journal PolygonNumber of Angles Sum of degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6710 Heptagon7890 (n-2)180 = Sum of degrees