Understand and use the sum of exterior x, and angles of any polygon · 2020-04-28 · 1 The diagram...
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1 The diagram shows an interior angle of a hexagon and its adjacent exterior angle. a) Talk to a partner about why you think they are called interior and exterior angles. b) Choose from the list to complete the sentences. adjacent interior exterior straight sum 180° An angle and its angle form a line. Therefore they to c) Complete the statement. interior angle + exterior angle = 2 ABC is an equilateral triangle. a) Explain why each of the interior angles is 60°. b) x, y and z are the exterior angles of triangle ABC. Work out the sizes of these angles. x = y = z = c) Complete the calculation. x + y + z = d) Work out the exterior angles of each triangle. Label them on the diagram and complete the calculations. x + y + z = x + y + z = x + y + z = 3 Work out the size of the exterior angle of each polygon. Then work out the sum of the exterior angles. a) a = b = c = d = a + b + c + d = Understand and use the sum of exterior angles of any polygon © White Rose Maths 2020 exterior interior y x A C B z 60° 60° 60° y x z 70° 45° 65° y x z 80° 50° 50° y x z 35° 65° 80° a b c d 50° 50° 130° 130°
Transcript of Understand and use the sum of exterior x, and angles of any polygon · 2020-04-28 · 1 The diagram...
1 Thediagramshowsaninteriorangleofahexagonanditsadjacent
exteriorangle.
a) Talktoapartneraboutwhyyouthinktheyarecalledinteriorand
exteriorangles.
b) Choosefromthelisttocompletethesentences.
adjacent interior exterior straight sum 180°
An angleandits
angleforma line.Thereforethey
to
c) Completethestatement.
interiorangle+exteriorangle=
2 ABCisanequilateraltriangle.
a) Explainwhyeachoftheinterioranglesis60°.
b) x,yandzaretheexterioranglesoftriangleABC.
Workoutthesizesoftheseangles.
x= y= z=
c) Completethecalculation. x+y+z=
d) Workouttheexterioranglesofeachtriangle.Labelthemonthe
diagramandcompletethecalculations.
x+y+z= x+y+z=
x+y+z=
3 Workoutthesizeoftheexteriorangleofeachpolygon.
Thenworkoutthesumoftheexteriorangles.
a) a=
b=
c=
d=
a+b+c+d=
Understand and use the sumofexterior anglesofany polygon
©WhiteRoseMaths2020
exteriorinterior
y
x
AC
B
z
60°
60° 60°
y
x
z
70°
45° 65°
yx
z
80°
50°50°
y
x
z
35°65°
80°
a
b
c
d50°50°
130° 130°
b) a=
b=
c=
d=
� e�=
a+b+c+d+e=
Whatdoyounotice?
4 Completethesentence.
Thesumoftheexterioranglesofanypolygonis
5 Workoutthesizesoftheunknownangles.
a) c)�
a= c=
b) d)�
b= d=
6 Workoutthesizeoftheexterioranglesofregularpolygonswiththe
givennumberofsides.
a) 3sides c)5sides e)10sides
b) 4sides d)6sides f)36sides
7 Aregularpolygonhasnsides.
a) Writeanexpressionforthesizeofeachexteriorangle.
�
b) Writeanexpressionforthesizeofeachinteriorangle.
�
8 Aregularpolygonhasanexteriorangleof30°.
Howmanysidesdoesthepolygonhave?
�
©WhiteRoseMaths2020
ab
d
ec
80°
140°
140°
a
100°150°
d
67°
125°
62°
80°
b
80° 60°
70°
65°
c
c
97°
83°25°
45°
