Cambridge International Mathematics

Lines, angles and polygons (Chapter 4) 107

The sum of the exterior angles of any polygon is always 360 o.

This fact is useful for finding the size of an interior angle of a regular polygon.

Example 6 Self Tutor

A regular polygon has 15 sides. Calculate the size of each interior angle.

For a 15 -sided polygon, each exterior angle is 360 o¥15 = 24o

) each interior angle is 180 o¡ 24 o= 156o

EXERCISE 4E

1 Solve forx:

abc

2 Calculate the size of each interior angle of these regular polygons:

a with 5 sides b with 8 sides c with 10 sides

d with 20 sides e with 100 sides f withnsides

3 Calculate the number of sides of a regular polygon given that an exterior angle is:

a 45 o b 15 o c 2 o d^12 o

4 Calculate the number of sides of a regular polygon with an interior angle of:

a 120 o b 150 o c 175 o d 179 o

Review set 4A

#endboxedheading

1 Copy and complete: If two parallel lines are cut by a third line then:

a the alternate angles are ......

b co-interior angles are ......

2 Find the value of the unknown, giving reasons for your answer:

abc

x° 150°

80°

75°

x°

110°

x°

x°

x°

x°

x°

x°

72°

x° 2°x 50°

25°

43°

50°

x°

From the Discovery, you should have found that:

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_04\107IGCSE01_04.CDR Monday, 27 October 2008 1:43:21 PM PETER