Cambridge International Mathematics

94 Lines, angles and polygons (Chapter 4)

² Two angles which have the same vertex and share a common

arm are calledadjacent angles.

PbAQ and QAR are adjacent angles.b

² For intersecting lines, angles which are directly opposite each

other are calledvertically opposite angles.

The following properties can be used to solve problems involving angles:

Title Figure

Angles centred at a point The sum of the sizes of the angles at a

point is 360 o:

a+b+c= 360

Adjacent angles on a

straight line

The sum of the sizes of the angles on a line

is 180 o. The angles are supplementary.

a+b= 180

Adjacent angles in a right

angle

The sum of the sizes of the angles in

a right angle is 90 o. The angles are

complementary.

a+b=90

Vertically opposite angles Vertically opposite angles are equal in

size.

a=b

Corresponding angles When twoparallel lines are cut by a

third line, then angles in corresponding

positions are equal in size.

a=b

Alternate angles When twoparallellines are cut by a third

line, then angles in alternate positions are

equal in size.

a=b

A

P

Q

R

a°c°b°

a°b°

a°

b°

a°

b°

a°

b°

a°

b°

Property

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