Angles in Polygons & Parallel Lines

and  are straight lines.
is parallel to .

Angle 
Angle 

Work out the size of the angle marked .
Give reasons for each stage of your working.

and  are parallel straight lines.
 is a straight line.

Work out the value of .
Give reasons for your answer.

and  are parallel lines.
is a straight line.

Angle .
Angle .

Work out the size of the angle marked .
Give reasons for each stage of your working.

The diagram shows a regular octagon and a regular hexagon.

Find the size of the angle marked .
You must show all your working.

and  are regular pentagons.

is parallel to .

Work out the size of angle .
You must show all your working.

and  are 2 sides of a regular 12-sided polygon.
 is a diagonal of the polygon.

Work out the size of angle .
You must show your working.

 is a straight line.
 is parallel to .
.

Work out the size of the angle marked .
You must give reasons for your answer.

is a pentagon.

Angle  angle .

Work out the size of angle .
You must show all your working.

Here is a 10-sided polygon.

Work out the value of 

................................................. 

Each interior angle of a regular polygon is 162°

Work out the number of sides the polygon has.

The diagram shows a triangle.

Work out the value of .

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

The diagram shows a parallelogram  and an isosceles triangle  in which 

and  are straight lines.
Angle 

Work out the size of angle 
Give a reason for each stage of your working.

What is the size of an exterior angle of a regular decagon?

Circle your answer.

The exterior angle of a regular polygon is 45°

Circle the name of the regular polygon.

Part of a regular polygon with 15 sides is shown.

Work out the size of an interior angle.

....................................................degrees 

The sum of the angles in any quadrilateral is 360°

For example, in a rectangle 4 × 90° = 360°

Zak writes,

   5 × 90° = 450° so the sum of the angles in any pentagon must be 450°

Is he correct?

Tick a box.

       Yes          No

Show working to support your answer.

Here is a sketch of a quadrilateral.

All lengths are in centimetres.

Tick one box for each statement.

Tick all the statements that are true for any rhombus.

 The diagonals are lines of symmetry

 The diagonals bisect each other

 The diagonals are perpendicular

 The diagonals are equal in length

Work out the size of the exterior angle of a regular 12-sided polygon.

Use your answer to part (a) to write down the size of the interior angle of a regular 12-sided polygon.

The diagram shows triangle ABC.
CD is parallel to AB.
A, C and E lie in a straight line.
Angles of size and are shown.

Insert  ° or to make this statement true.
Give a reason for your answer.

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

Use the diagram and the answer to part (a) to show that the angles of a triangle add up to 180°.

Give a reason for each statement you make.

Here is a pentagon .

 is a kite.

Angle 
Angle 
Angle 

Work out the size of angle .

 is a regular 9-sided polygon.

The vertices  and  are joined with a straight line.

Work out the size of angle .
You must show how you get your answer.

The diagram shows a hexagon.
The hexagon has one line of symmetry.

Angle 

Angle  angle .

Work out the size of angle .
You must show all your working.

 is a regular pentagon.
and  are points on a circle, centre .
and  are tangents to the circle.
 is a straight line.

Prove that .

The diagram shows a regular 10-sided polygon,

Show that .

The diagram shows a regular octagon and a regular pentagon

Work out the size of the angle.

and are four of the sides of a regular decagon.

Work out the size of angle .

..............................degrees 

and are straight lines.

Ava assumes that and are parallel.

What answer should she get for the size of angle ?

...............................degrees 

In fact,

and are not parallel
angle is 60°

What effect does this have on the size of angle ?
Tick a box.

	is bigger
	is the same
	is smaller

Show working to support your answer.

and are straight lines.

All angles are in degrees.

Show that is parallel to .

Imran joins two tiles together as shown below.
One tile is a regular hexagon and the other tile is a regular pentagon.

Show that angle  is 132°.

Imran thinks that another tile in the shape of a regular polygon will fit exactly into angle .

Is Imran correct?
Show your reasoning.

Angle BAE is part of a regular 18-sided polygon.
Angle CAD is part of a regular 10-sided polygon.
The dashed line through A is a line of symmetry of both polygons.

Work out angle BAC.