Angles in special quadrilaterals - Swaythling Primary · 2020. 4. 23. · 1 The sum of the interior...
Transcript of Angles in special quadrilaterals - Swaythling Primary · 2020. 4. 23. · 1 The sum of the interior...
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Angles in special quadrilaterals
1 Workoutthesumoftheanglesineachshape.
a) b)
Whatdoyounotice?
2 Thediagramsshowthefourverticesofaquadrilateralarranged
aroundapoint.
Whatdothediagramsillustrateaboutthesumoftheanglesin
aquadrilateral?
Completethesentence.
Anglesinaquadrilateral©WhiteRoseMaths2020
3 Workoutthesizeoftheunknownangleineachtrapezium.
a) b)
a= b=
c) Whatisthesameandwhatisdifferentaboutthetrapeziums?
4 Workoutthesizesoftheunknownangles.
a) b)
c= d=
c) Whatdoyounoticeaboutoppositeanglesinaparallelogram?
a
a
b
b
c
cd
d
a b
63° 123°
57°
123°
cd45°
45°135°
78° 102°
78°
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5 Twoisoscelestrianglesarejoinedtoformakite.
a) Workoutthesizesoftheunknownangles.
w= y= x= z=
b) Workoutw+x.
c) Workouty+z.
Whatdoyounotice?Talkaboutitwithapartner.
6 Workoutthesizesoftheunknownangles.
a) b)
r= s=
©WhiteRoseMaths2020
c) d)
t= u=
Compareyourreasoningwithapartner.
7 Teddyisdrawingaquadrilateral.
IsTeddy’squadrilateralpossible?
Explainyouranswer.
My quadrilateral has exactly three right-angles.
104°
68°
wx
yz
91°
87°
113°
73°r
s
107° 61°t
u
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1 Thesumoftheinterioranglesofatriangleis180°.
Splitthepolygonsintotrianglestoworkoutthesumoftheir
interiorangles.Yourlinesshouldnotoverlap.
Thefirstonehasbeendoneforyou.
a) numberofsides= 5
numberoftriangles= 3
3×180= 540
Thesumoftheinterioranglesofapentagonis 540°
b) numberofsides=
numberoftriangles=
×180=
Thesumoftheinterioranglesofahexagonis
c) numberofsides=
numberoftriangles=
×180=
Thesumoftheinterioranglesofaheptagonis
Whatdoyounoticeaboutthenumberofsidescompared
tothenumberoftriangles?
Angles in regularpolygons
©WhiteRoseMaths2020
2 Completethetable.
ShapeNumberof
sides
Numberof
triangles
Sumofinterior
angles
quadrilateral 3 2 360°
pentagon
nonagon
decagon
6
6
1,800°
Compareanswerswithapartner.
3 Daniisworkingoutthesumoftheinterioranglesofapolygon.
Hereareherworkings.
DoyouagreewithDani?
Explainyouranswer.
10 × 180 = 1,800°
1 26
4
5
3
7
8
9 10
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4 Rosie,AmirandEvaaredrawingpolygons.
a)
WhatpolygonhasRosiedrawn?
b)
WhatpolygonhasAmirdrawn?
c)
WhatisthesumoftheinterioranglesofEva’spolygon?
©WhiteRoseMaths2020
5 Eachcompoundshapeismadeupofregularpolygons.
Workoutangleyineachcase.
a) d)
y= y=
b) e)
y= y=
c) f)
y= y=
The sum of the interior angles of my polygon
is 1,080°.
I have split my polygon into four triangles.
My polygon has more sides than Rosie’s but fewer
than Amir’s.
Rosie
Eva
Amir
y
y
y
y
y
y
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1 2
Modelled solutions are on the video
145 cars
264 sweets
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3 4
Modelled solutions are on the video
10p × 22
20p × 115p × 33
Various combinations
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1 2
14 cm 80 cm²
Modelled solutions are on the video
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3 4
£ 9.70
£ 8.50Modelled solutions are on the video