Thurs Nov 17th – Angles in Polygons

LEARNING OBJECTIVE: To derive the rules for angles in regular and irregular polygons

SUCCESS CRITERIA: You will derive rules for the following:

1. Sum of all the angles in any polygon
   
2. Interior angle of a regular polygon
   
3. Exterior angle of a regular polygon
   

STARTER:

Complete the names of all the polygons on this sheet:

Number of sides	Name	No Of Triangles	Sum Of Interior Angles	One angle of Regular Polygon	Exterior angle of Regular Polygon	Exterior angle multiplied by number of sides
3	Triangle	1	1x180=180	60	120	360
4	Quadrilateral	2	2x180=360	90	90	360
5	Pentagon	3	3x180 = 540	108	72	360
6	Hexagon	4	4 x 180 = 720	120	60	360
7	Septagon	5	5 x 180 = 900	128.571428	51.43(2dp)	360
8	Octagon	6	6 x 180 = 1080	135	45	360
9	Nonagon	7	7x180 = 1260	140	40	360
10	Decagon	8	8x180 = 1440	144	36	360
12	Dodecagon	10	10 x 180 = 1800	150	30	360
20	Icosagon	18	18x 180 = 3240	162	18	360
N - sides	No Name	n-2	180x(n-2)	180x(n-2)/n	180 - 180(n-2)/n	360

 
 

Names of Polygons

NOTES: A regular polygon has Equal angles and equal length sides

LESSON:

Look at building up total angles inside a polygon using the 'Number of triangles' method.

Demonstrate using triangle, quadrilateral and pentagon on the IWB

Get students to complete the table, adding the columns

Number of Triangles, Sum of All Angles, One Interior angle of a regular polygon

TASK 1: Now complete the table for the rest of the polygons including n-sides.

PLENARY: Discussion on results and entries for n – sides – encourage answers/descriptions from students

Explain what is meant by the external angle(supplementary angle) ie interior + exterior angle = 180

TASK 2 Add these columns to your table and complete for ALL rows:

One Exterior Angle of a regular polygon, Sum of all exterior Angles, Sum of all Angles / 360

Explain your findings IN YOUR OWN WORDS

PLENARY: Discussion on results