Angles in special quadrilaterals - Swaythling Primary · 2020. 4. 23. · 5 Each compound shape is...

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Angles in special quadrilaterals 1 Work out the sum of the angles in each shape. a) b) What do you notice? 2 The diagrams show the four vertices of a quadrilateral arranged around a point. What do the diagrams illustrate about the sum of the angles in a quadrilateral? Complete the sentence. Angles in a quadrilateral © White Rose Maths 2020 3 Work out the size of the unknown angle in each trapezium. a) b) a = b = c) What is the same and what is different about the trapeziums? 4 Work out the sizes of the unknown angles. a) b) c = d = c) What do you notice about opposite angles in a parallelogram? a a b b c c d d a b 63° 123° 57° 123° c d 45° 45° 135° 78° 102° 78°

Transcript of Angles in special quadrilaterals - Swaythling Primary · 2020. 4. 23. · 5 Each compound shape is...

  • 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°

  • 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

  • 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 4 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

  • 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

  • 1 2

  • 3 4

  • 1 2

  • 3 4


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