Angles in Polygons & Parallel Lines (Edexcel GCSE Maths: Higher)

 is a parallelogram.

Angle .
Angle .
Angle .

Calculate the size of angle .
You must give reasons for your answer.

is parallel to .

Angle 

Work out the size of the angle marked .
Give reasons for your answer.

and  are parallel lines.

Angle 

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

and  are parallel lines.
and  are straight lines.

Angle 
Angle 

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

and  are straight lines.
and  are parallel.
Angle 
Angle 

Work out the size of the angle marked .
Give reasons for your answer.

 is a parallelogram.
 is a straight line.
is the point on  so that  is a straight line.

Angle 
Angle 

Show that angle 
Give a reason for each stage of your working.

and  are parallel.
.
Angle  angle 

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

The diagram shows a pattern using four identical rhombuses.

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

 is a regular octagon.
is a hexagon.

 is a line of symmetry of the hexagon.
Angle   angle 

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

The diagram shows part of a pattern made from tiles.

The pattern is made from two types of tiles, tile A and tile B.

Both tile A and tile B are regular polygons.

Work out the number of sides tile A has.

 is a regular pentagon.
 is a square.

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

 is a regular octagon.
and  are two identical regular pentagons.

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

In the diagram, ,  and  are three sides of a regular polygon P.

Show that polygon P is a hexagon.
You must show your working.

Here is a parallelogram.

Work out the value of  and the value of .

The diagram shows a square and 4 regular pentagons.

Work out the size of the angle marked .

and  are parallel lines.
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.

 is a regular pentagon.
and  are straight lines.

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

An interior angle of an isosceles triangle is p° and an exterior angle is q °.

It is given that q = 5p .
Write the ratio p : q in its simplest form.

Work out the two different possible sets of angles for the isosceles triangle.

Triangle 1: ............°, .............°, .............°
Triangle 2: ............°, .............°, .............°

Here is a quadrilateral.

and

Show that

The diagram shows a regular pentagon.
and  are two of the lines of symmetry of the pentagon.

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

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 

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.

AB, CD and EF are straight lines.

Ava assumes that AB and CD are parallel.
What answer should she get for the size of angle ?

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

In fact,

AB and CD are not parallel
angle is 60°

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

Show working to support your answer.

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.

AB, CD and YZ are straight lines.
All angles are in degrees.

Show that AB is parallel to CD.