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.

Part of a regular polygon with 15 sides is shown.

Work out the size of an interior angle.

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

The diagram shows a triangle.

Work out the value of .

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

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.

Here is a 10-sided polygon.

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.

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.

Each interior angle of a regular polygon is 162°

Work out the number of sides the polygon has.

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

Circle your answer.

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.

The exterior angle of a regular polygon is 45°

Circle the name of the regular polygon.

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.

	is bigger
	is the same
	is smaller

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.