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Investigation: Total Interior Angle in a Polygon

Last updated over 3 years ago

16 Nsɛmmisa

In this exercise, you will figure out a general rule to describe the sum of internal angles in a triangle.

Step 1:

Split each diagram into triangles in such a way that you are only splitting the angles at each vertex.

Step 2:

Use your understanding of the sum of the interior angles of a triangle to find the total interior angle of the shape in question.

Step 3:

Compare all the values of every shape and figure out a general rule for a polynomial of any number of sides.

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1.

Use a single line to break the quadrilateral into 2 triangles.

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2.

Hence calculate the sum of the total interior angles of a quadrilateral.

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3.

Use two lines to break the pentagon into 3 triangles.

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4.

Hence calculate the sum of the total interior angles of a pentagon.

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5.

Use three lines to break the hexagon into 4 triangles.

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6.

Hence calculate the sum of the total interior angles of a hexagon.

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7.

Use four lines to break the heptagon into 5 triangles.

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8.

Hence calculate the sum of the total interior angles of a heptagon.

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9.

Use five lines to break the octagon into 6 triangles.

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10.

Hence calculate the sum of the total interior angles of an octagon.

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11.

Use six lines to break the nonagon into 7 triangles.

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12.

Hence calculate the sum of the total interior angles of a nonagon.

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13.

Use seven lines to break the decagon into 8 triangles.

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14.

Hence calculate the sum of the total interior angles of a decagon.

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15.

Complete the table below using the information you gathered so far.

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16.

What connection can you see between the number of triangles, the number of sides of a polygon and the total interior angle? Can you write the relationship as an equation?