and are parallel lines.
 is a straight line.
Angle .
Work out the size of the angle marked .
Give reasons for your answer.
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and are parallel lines.
 is a straight line.
Angle .
Work out the size of the angle marked .
Give reasons for your answer.
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and are straight lines.
is parallel to .
AngleÂ
AngleÂ
Work out the size of the angle marked .
Give reasons for each stage of your working.
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and are parallel straight lines.
 is a straight line.
Work out the value of .
Give reasons for your answer.
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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.
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The diagram shows a regular octagon and a regular hexagon.
Find the size of the angle marked .
You must show all your working.
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and are regular pentagons.
is parallel to .
Work out the size of angle .
You must show all your working.
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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.
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 is a straight line.
 is parallel to .
.
Work out the size of the angle marked .
You must give reasons for your answer.
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is a pentagon.
Angle angle .
Work out the size of angle .
You must show all your working.
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Here is a 10-sided polygon.
Work out the value ofÂ
.................................................Â
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Each interior angle of a regular polygon is 162°
Work out the number of sides the polygon has.
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The diagram shows a triangle.
Work out the value of .
= ..................
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The diagram shows a parallelogram and an isosceles triangle in whichÂ
and are straight lines.
AngleÂ
Work out the size of angleÂ
Give a reason for each stage of your working.
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What is the size of an exterior angle of a regular decagon?
Circle your answer.
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The exterior angle of a regular polygon is 45°
Circle the name of the regular polygon.
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Part of a regular polygon with 15 sides is shown.
Work out the size of an interior angle.
....................................................degreesÂ
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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.
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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 | Â | Â | Â |
The quadrilateral is a parallelogram | Â | Â | Â |
The quadrilateral is a rhombus | Â | Â | Â |
The quadrilateral is a kite | Â | Â | Â |
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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
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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.
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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.
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 is a parallelogram.
Angle .
Angle .
Angle .
Calculate the size of angle .
You must give reasons for your answer.
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is parallel to .
AngleÂ
Work out the size of the angle marked .
Give reasons for your answer.
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and are parallel lines.
AngleÂ
Work out the size of the angle marked .
Give reasons for each stage of your working.
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and are parallel lines.
and are straight lines.
AngleÂ
AngleÂ
Work out the size of the angle marked .
Give a reason for each stage of your working.
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and are straight lines.
and are parallel.
AngleÂ
AngleÂ
Work out the size of the angle marked .
Give reasons for your answer.
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 is a parallelogram.
 is a straight line.
is the point on so that is a straight line.
AngleÂ
AngleÂ
Show that angleÂ
Give a reason for each stage of your working.
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and are parallel.
.
Angle angleÂ
Work out the size of the angle marked .
You must show your working.
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The diagram shows a pattern using four identical rhombuses.
Work out the size of the angle marked .
You must show your working.
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 is a regular octagon.
is a hexagon.
 is a line of symmetry of the hexagon.
Angle  angleÂ
Work out the size of angle .
You must show all your working.
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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.
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 is a regular pentagon.
 is a square.
Work out the size of angle .
You must show all your working.
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 is a regular octagon.
and are two identical regular pentagons.
Work out the size of the angle marked .
You must show all your working.
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In the diagram, , and are three sides of a regular polygon P.
Show that polygon P is a hexagon.
You must show your working.
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Here is a parallelogram.
Work out the value of and the value of .
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The diagram shows a square and 4 regular pentagons.
Work out the size of the angle marked .
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and are parallel lines.
and are parallel lines.
 is a straight line.
AngleÂ
AngleÂ
Work out the size of the angle marked .
Give reasons for each stage of your working.
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 is a regular pentagon.
and are straight lines.
Work out the size of angle .
You must show how you got your answer.
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Here is a quadrilateral.
and
Show that
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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: ............°, .............°, .............°
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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.
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Here is a pentagon .
 is a kite.
AngleÂ
AngleÂ
AngleÂ
Work out the size of angle .
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 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.
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The diagram shows a hexagon.
The hexagon has one line of symmetry.
AngleÂ
Angle angle .
Work out the size of angle .
You must show all your working.
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 is a regular pentagon.
and are points on a circle, centre .
and are tangents to the circle.
 is a straight line.
Prove that .
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The diagram shows a regular 10-sided polygon,
Show that .
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The diagram shows a regular octagon and a regular pentagon
Work out the size of the angle.
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and are four of the sides of a regular decagon.
Work out the size of angle .
..............................degreesÂ
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and are straight lines.
Ava assumes that and are parallel.
What answer should she get for the size of angle ?
...............................degreesÂ
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.
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and are straight lines.
All angles are in degrees.
Show that is parallel to .
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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.
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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.
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