Cambridge International Mathematics

104 Lines, angles and polygons (Chapter 4)

You should have discovered that:

The sum of the interior angles of anyn-sided polygon is (n¡2)£ 180 o.

Example 5 Self Tutor

Findx, giving a brief reason:

The pentagon has 5 sides

) the sum of interior angles is 3 £ 180 o= 540o

) x+x+x+ 132 + 90 = 540

) 3 x+ 222 = 540

) 3 x= 318

) x= 106

EXERCISE 4D

1 Find the sum of the interior angles of:

a a quadrilateral b a pentagon c a hexagon d an octagon.

2 Find the value of the unknown in:

abc

de f

3 Find the value ofxin each of the following, giving a reason:

abc

121°

x° 62°

126° 119°

x° 72°

150°

105° x°

x°

x°

x°

x°

132°

a°

108°

108°

108° 108°

a°

85°

100°

130°

2 x° 2 x°

2 x°

x°

2 x°

x°

x°

120° x°

150°

2 x° 2°x

x°

x° x°

3°x

a°

120°

140°

145°

105°

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Y:\HAESE\IGCSE01\IG01_04\104IGCSE01_04.CDR Friday, 12 September 2008 4:01:21 PM PETER