Angles in Polygons & Parallel Lines (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.

Find the value of .

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

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

Find the size of one interior angle of a regular 10-sided polygon.

A triangle is isosceles.
One of its angles is 96°.

Find the other two angles.

........................ and ........................

Find the value of .

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

Work out the size of one interior angle of a regular polygon with 20 sides.

The diagram shows a right-angled triangle .
Calculate the length of .

= ................................................m

The diagram shows an isosceles triangle  with 
and  are straight lines and  is parallel to .
Angle .
Find the value of and the value of .

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

Work out the size of an interior angle of a regular 20-sided polygon.

Work out the size of one exterior angle of a regular octagon.

Find the size of one interior angle of a regular decagon.

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 .

Work out angle .

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.

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

Find the value of

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

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 

a)

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

[2]

b)

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

[2]

Work out the value of and the value of .

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

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

[2]

Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.

The diagram shows two parallel lines  and .
and angle .

Find the value of .

............................. 

The diagram shows a circle, centre  and diameter .
is a tangent to the circle at .
is parallel to , angle  and angle  = angle .

Write down the mathematical name of the polygon .

[1]

Explain why angle is a right angle.

[1]

Find angle , giving a reason for your answer.

Angle  =....................... because ....................... [2]

Complete the statements.

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

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