1 Thesumoftheinterioranglesofatriangleis180°.

Splitthepolygonsintotrianglestoworkoutthesumoftheirinteriorangles.

Yourlinesshouldnotoverlap.

Thefirstonehasbeendoneforyou.

a) numberofsides= 5

numberoftriangles= 3

3×180= 540

Thesumoftheinterioranglesofapentagonis 540°b) c)

Whatdoyounoticeaboutthenumberofsidescompared

tothenumberoftriangles?

2 Completethetable.

ShapeNumberof

sidesNumberoftriangles

Sumofinteriorangles

quadrilateral 4 2 360°

pentagon

nonagon

decagon

6

6

1,800°

Compareanswerswithapartner.

3 Daniisworkingoutthesumoftheinterioranglesofapolygon.

Hereareherworkings.

10 × 180 = 1,800°

1 26

4

5

3

7

8

9 10

DoyouagreewithDani?

Explainyouranswer.

4 Rosie,AmirandEvaaredrawingpolygons.

a)

I have split my polygon into four triangles.

Rosie

WhatpolygonhasRosiedrawn?

b)

The sum of the interior angles of my polygon

is 1,080°.

Amir

WhatpolygonhasAmirdrawn?

Angles in regular polygons

©WhiteRoseMaths2020

c)

My polygon has more sides than Rosie’s but fewer

than Amir’s.

Eva

WhatisthesumoftheinterioranglesofEva’spolygon?

5 Eachcompoundshapeismadeupofregularpolygons.

Workoutangleyineachcase.

a) d)

y

y

b) e)

y

y

c) f)

y

y

Angles in regular polygons

©WhiteRoseMaths2020

3 Daniisworkingoutthesumoftheinterioranglesofapolygon.

Hereareherworkings.

10 × 180 = 1,800°

1 26

4

5

3

7

8

9 10

DoyouagreewithDani?

Explainyouranswer.

4 Rosie,AmirandEvaaredrawingpolygons.

a)

I have split my polygon into four triangles.

Rosie

WhatpolygonhasRosiedrawn?

b)

The sum of the interior angles of my polygon

is 1,080°.

Amir

WhatpolygonhasAmirdrawn?