Angles in Polygons & Parallel Lines (Cambridge (CIE) IGCSE Maths: Core)

The diagram shows a triangle drawn between a pair of parallel lines.

Find the value of and the value of .

A regular polygon has an exterior angle of 20°.

Work out the number of sides of this polygon.

The diagram shows two parallel lines and two straight lines.

i) Find the value of .
Give a reason for your answer.
a = ................ because ..................................................................................................... [2]

ii) Find the value of .
Give a reason for your answer.
b = ................ because ......................................................................................................[2]

iii) Find the value of .

= ................................................. [2]

In the diagram, is parallel to .

Find the value of.
Give a geometrical reason for your answer.

= ......................... because ....................................

Work out the value of .
Give a geometrical reason for your answer.

.................because ......................

Work out the value of

i)

=..........................[1]

ii)

...........................[1]

The diagram shows a triangle between two parallel lines, and .

Find the value of

i)

=............................. [1]

ii)

............................. [1]

iii) .

= .............................  [1]

Complete the statements.

............................ because ............................   

........................... because ............................ 

is a rectangle.
is parallel to .

Find the value of and the value of .

= ......................................................

= ................................................. .....

Two regular octagons and a square meet at point .
Show, by calculation, that the three interior angles at add up to 360°.

The diagram shows two pairs of parallel lines.

Find the value of , the value of and the value of .

The diagram shows part of a different regular polygon.

is an exterior angle.
is an interior angle.
The ratio .

i) Work out angle .

[3]

ii) Work out the number of sides of this regular polygon.

[1]

is a pentagon.

Explain why the diagram shows that the sum of the interior angles of a pentagon is 540°. Do not measure any angles.

In the diagram and are straight lines.
Lines and are parallel.

Find angle and give a reason for your answer.

Angle = ................................. because ...................................

The diagram shows two regular pentagons.
Pentagon  is an enlargement of pentagon , centre .

Find angle .

Angle  = .............................. 

In the diagram,  is a straight line.
is parallel to , angle  = 34° and 

i) Complete the statements.

a) ................ because ................................

[2]

b) ................ because .................................

[2]

ii) Work out the value of and the value of .

.................... 

    .................... [2]

iii) Find the value of t and give a reason for your answer.

................ because ........................

[2]

Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.