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Now let’s explore the sum of the 4 angles in any quadrilateral.
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Any convex quadrilateral can be split into 2 triangles.
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If each triangle consists of 180, then 2 triangles would total 360.
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This can easily be seen in the square.
90 + 90 + 90 + 90 = 360 90 90 90 90
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Any convex pentagon can be split into 3 triangles.
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Each triangle consists of 180.
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180 + 180 + 180 = 540 180 180 180
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Now let’s chart our findings.
Polygon Sum of all angles triangle 180 quadrilateral 360 pentagon 540
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Do you notice any pattern?
Polygon Sum of all angles triangle 180 quadrilateral 360 pentagon 540
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As the number of sides on the polygons increase by 1 side, the sum of the angles increases by 180.
Sum of all angles triangle 180 quadrilateral 360 pentagon 540 + 180 + 180
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What is the sum of all angles in a convex hexagon?
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hexagon Polygon Sum of all angles triangle 180 quadrilateral 360
pentagon 540 hexagon
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hexagon 720 Polygon Sum of all angles triangle 180 quadrilateral
360 pentagon 540 hexagon 720
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