and are parallel lines.
is a straight line.
Angle .
Work out the size of the angle marked .
Give reasons for your answer.
Did this page help you?
and are parallel lines.
is a straight line.
Angle .
Work out the size of the angle marked .
Give reasons for your answer.
Did this page help you?
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.
Did this page help you?
and are parallel straight lines.
is a straight line.
Work out the value of .
Give reasons for your answer.
Did this page help you?
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.
Did this page help you?
The diagram shows a regular octagon and a regular hexagon.
Find the size of the angle marked .
You must show all your working.
Did this page help you?
and are regular pentagons.
is parallel to .
Work out the size of angle .
You must show all your working.
Did this page help you?
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.
Did this page help you?
is a straight line.
is parallel to .
.
Work out the size of the angle marked .
You must give reasons for your answer.
Did this page help you?
is a pentagon.
Angle angle .
Work out the size of angle .
You must show all your working.
Did this page help you?
Here is a 10-sided polygon.
Work out the value of
.................................................
Did this page help you?
Each interior angle of a regular polygon is 162°
Work out the number of sides the polygon has.
Did this page help you?
The diagram shows a triangle.
Work out the value of .
= ..................
Did this page help you?
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.
Did this page help you?
What is the size of an exterior angle of a regular decagon?
Circle your answer.
Did this page help you?
The exterior angle of a regular polygon is 45°
Circle the name of the regular polygon.
Did this page help you?
Part of a regular polygon with 15 sides is shown.
Work out the size of an interior angle.
....................................................degrees
Did this page help you?
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.
Did this page help you?
Here is a sketch of a quadrilateral.
All lengths are in centimetres.
Tick one box for each statement.
True | May be true | Not true | |
The quadrilateral is a rectangle | |||
The quadrilateral is a parallelogram | |||
The quadrilateral is a rhombus | |||
The quadrilateral is a kite |
Did this page help you?
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
Did this page help you?
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.
Did this page help you?
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.
Did this page help you?
is a parallelogram.
Angle .
Angle .
Angle .
Calculate the size of angle .
You must give reasons for your answer.
Did this page help you?
is parallel to .
Angle
Work out the size of the angle marked .
Give reasons for your answer.
Did this page help you?
and are parallel lines.
Angle
Work out the size of the angle marked .
Give reasons for each stage of your working.
Did this page help you?
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.
Did this page help you?
and are straight lines.
and are parallel.
Angle
Angle
Work out the size of the angle marked .
Give reasons for your answer.
Did this page help you?
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.
Did this page help you?
and are parallel.
.
Angle angle
Work out the size of the angle marked .
You must show your working.
Did this page help you?
The diagram shows a pattern using four identical rhombuses.
Work out the size of the angle marked .
You must show your working.
Did this page help you?
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.
Did this page help you?
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.
Did this page help you?
is a regular pentagon.
is a square.
Work out the size of angle .
You must show all your working.
Did this page help you?
is a regular octagon.
and are two identical regular pentagons.
Work out the size of the angle marked .
You must show all your working.
Did this page help you?
In the diagram, , and are three sides of a regular polygon P.
Show that polygon P is a hexagon.
You must show your working.
Did this page help you?
Here is a parallelogram.
Work out the value of and the value of .
Did this page help you?
The diagram shows a square and 4 regular pentagons.
Work out the size of the angle marked .
Did this page help you?
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.
Did this page help you?
is a regular pentagon.
and are straight lines.
Work out the size of angle .
You must show how you got your answer.
Did this page help you?
Here is a quadrilateral.
and
Show that
Did this page help you?
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: ............°, .............°, .............°
Did this page help you?
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.
Did this page help you?
Here is a pentagon .
is a kite.
Angle
Angle
Angle
Work out the size of angle .
Did this page help you?
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.
Did this page help you?
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.
Did this page help you?
is a regular pentagon.
and are points on a circle, centre .
and are tangents to the circle.
is a straight line.
Prove that .
Did this page help you?
The diagram shows a regular 10-sided polygon,
Show that .
Did this page help you?
The diagram shows a regular octagon and a regular pentagon
Work out the size of the angle.
Did this page help you?
and are four of the sides of a regular decagon.
Work out the size of angle .
..............................degrees
Did this page help you?
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.
Show working to support your answer.
Did this page help you?
and are straight lines.
All angles are in degrees.
Show that is parallel to .
Did this page help you?
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.
Did this page help you?
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.
Did this page help you?