Angles in Polygons Activity

Overview: Students investigate the interior angles of polygons and generalize to a pattern rule.

Curriculum Expectations:

• Measurement and Geometry: Determine, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems

Learning Goal:

• To explore/identify the relationship between the sum of the interior angles and the number of sides in a polygon.
  

Timing and sequencing: This activity will take one period. Introduction to geometric properties of polygons.

Classroom constructs: Students work in groups of 3

Materials:

• Protractors
• Scissors
• Paper
• Polygon shapes

Description:

In groups of 3, students brainstorm what they know about triangles and quadrilaterals (e.g. number of sides, sum of the interior angles, different types, etc)

Students will likely recall that the angles in a triangle add to 180o and that rectangles (and quadrilaterals) add up to 360o.

To confirm that the sum of the angles in a triangle add to 180o and that a straight line measures 180o: Have students draw a large triangle on a piece of paper and cut it out. Now, students tear off each corner of the triangle and rearrange the 3 “angles” so that their vertices meet at one point with no overlap.  What does this tell you about sum of the angles in the triangle?

To confirm that the sum of the angles in a quadrilateral add to 360o: Students draw a large quadrilateral on a piece of paper and cut it out. Now, students tear off each corner of the quadrilateral and rearrange the 4 “angles” so that their vertices meet at one point with no overlap.  What does this tell you about sum of the angles in the quadrilateral?

On the board, the teacher can make a table showing the type of polygon, number of sides and sum of interior angles. Students will complete the table using the information about triangles and quadrilaterals that we already have to look for a pattern in the sum of the interior angles.

e.g.

polygon	Number of sides	Sum of the interior angles
triangle	3	180
quadrilateral	4	360
pentagon	5	prediction?

Students will likely notice that the sum of the interior angles are increasing by 180o for every extra side added.

Have students make predictions for polygons with 5, 6, 7 and 8 sides.

In groups of 3, each student is given a polygon with 5, 6, 7 or 8 sides (a polygon with the same number of sides for each group). Students measure the interior angles with a protractor to confirm their predictions.

This will give an opportunity to discuss how to use a protractor and also why we might not get exactly the same sum of the angles as our prediction (measurement error).

Students will then come up with a general pattern rule/equation for determining the sum of the interior angles in a polygon using the table. Students will likely come up with

s=180n-360, where n is the number of sides

Resources