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?
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