Edexcel IGCSE Maths
Topic questions Geometry and measures Angle facts
56 questions · 229 marks · about 4.5 hours
AEC and BED are straight lines.
Sergio says that the value of x is 58
Give a reason why Sergio is correct.
In the diagram, GHIJ is a quadrilateral.
Chloe says “FGH is a straight line”
Show that Chloe is wrong. Give a reason for each stage of your working.
ABC and EBD are straight lines. Triangle BCD is isosceles with BD = BC
Angle ABE = 104
Work out the value of x
Here are two shapes.
Write down the mathematical name of the
triangle,
quadrilateral.
On the triangle, draw the line of symmetry.
Write down the order of rotational symmetry of the quadrilateral.
ABCD is a quadrilateral.
ADE is a straight line.
Work out the value of x Give a reason for each stage of your working.
The diagram shows a regular octagon.
Write down the number of lines of symmetry of a regular octagon.
Here is a shape.
On the shape, mark with a letter R a right angle.
On the shape, mark with a letter O an obtuse angle.
Find, by measuring, the size of the angle marked x
Work out the value of x
Give a reason for your answer.
ABDE is a quadrilateral. BCD is an isosceles triangle. ABC is a straight line.
Work out the value of y
ABCD is a quadrilateral. CDE is an isosceles triangle with CD = CE DEF is a straight line.
Work out the size of angle BCE Give a reason for each stage of your working.
angle = BCE........
Here is a centimetre grid.
On the grid, draw a right-angled triangle.
Here is a centimetre grid.
On the grid, draw a rectangle with an area of 20 cm2
ABCD and EFGH are straight lines. KFBJ and MGCL are parallel straight lines.
angle ABJ = 125° angle BFG = 32° angle FGM = x ° angle LCD = y °
Write down the value of x
Work out the value of y
Give a reason for your answer to (b) (i)
The diagram shows a 5-sided polygon, ABCDE
Write down the mathematical name for a 5-sided polygon.
Measure the length of the line AB Give your answer in centimetres.
On the diagram, mark an obtuse angle with the letter T
Also involves Geometric reasoning and proof
The diagram shows quadrilateral ABCD
ECD, BCF and GAD are straight lines.
Work out the value of x Give a reason for each stage of your working.
ABCD is a trapezium.
BC is parallel to AD
Find the size of the largest angle inside the trapezium.
BCD is an isosceles triangle with BD = CD ABC is a straight line. ABDE is a quadrilateral.
Work out the value of x Give a reason for each stage of your working.
Also involves Forming and solving equations
The diagram shows an isosceles triangle ABC
AB = 7 cm AC = BC = ycm
The area of the triangle is 42 cm2
Work out the value of y
Write down the mathematical name for an 8-sided polygon.
What type of angle is the angle marked x?
On the diagram above, draw a chord of the circle.
Change 3.6 metres into centimetres.
The diagram shows two parallel lines AB and DEF
BEG is a straight line.
angle DEG = 73° angle EBC = 124° angle ABC = w °
Work out the value of w Give reasons for each stage of your working.
AB, BC, CD, DE and EF are five sides of a regular polygon.
RST, SCU and BCV are straight lines. RST is parallel to CD Angle RSC = 128° Angle UCV = 32°
Work out how many sides the polygon has. Show your working clearly.
AB, BC, CD, DE and EF are five sides of a regular polygon.
RST, SCU and BCV are straight lines. RST is parallel to CD Angle RSC = 128° Angle UCV = 32°
Work out how many sides the polygon has. Show your working clearly.
ABC is a straight line.
Work out the value of x
Give a reason for your answer to (i)
CDE is an equilateral triangle. ABCF is a quadrilateral.
BCE and DCF are straight lines.
Work out the value of y You must show your working.
ACE and BCD are straight lines. AB is parallel to DE
Work out the value of x
Here are three shapes.
A B C
Shape A is a triangle.
Write down the mathematical name for this type of triangle.
Shape B is a rectangle.
On shape B, draw its lines of symmetry.
Shape C is a regular polygon.
Write down the order of rotational symmetry of shape C.
ABC is a straight line and BCD is a triangle.
Work out the value of x
PO, RO, SO and TO are four straight lines.
Work out the value of y
Give a reason for your answer.
The diagram shows isosceles triangle ABC
AB = AC = 17.5 cm
BC = 28 cm
Calculate the area of triangle ABC
Here is a quadrilateral.
What is the mathematical name of this quadrilateral?
Measure the size of the angle marked x.
On the quadrilateral, mark with arrows (
) a pair of parallel lines.
The quadrilateral has four angles.
How many of these angles are right angles?
The diagram shows quadrilateral ABCD and isosceles triangle ADE, where AE = AD.
EDC is a straight line.
Work out the value of x. Give a reason for each stage of your working.
Also involves Forming and solving equations
The diagram shows the isosceles triangle ABC in which AB = AC
BCD is a straight line.
Work out the value of x.
The diagram shows a regular pentagon, ABCDE, a regular hexagon, CFGHID, and a quadrilateral, EDIJ.
AEJ and HIJ are straight lines.
Work out the size of the angle marked x. Show your working clearly.
Also involves Rounding
Here is isosceles triangle ABC.
D is the midpoint of AC and DB = 16 cm.
Angle DAB = 65
Work out the perimeter of triangle ABC. Give your answer correct to one decimal place.
The diagram shows a regular pentagon, ABCDE, a regular hexagon, CFGHID, and a quadrilateral, EDIJ.
AEJ and HIJ are straight lines.
Work out the size of the angle marked x. Show your working clearly.
Here is isosceles triangle ABC.
D is the midpoint of AC and DB = 16 cm.
Angle DAB = 65
Work out the perimeter of triangle ABC. Give your answer correct to one decimal place.
ABD is a triangle.
AEDF, BCDG and HCEJ are straight lines. BA is parallel to HCEJ.
Work out the size of the angle marked x.
Here is a polygon with five sides.
Write down the mathematical name of a polygon with five sides.
Measure the size of the angle marked x.
Two sides of the polygon are parallel.
On the polygon, mark with arrows (>>) this pair of parallel lines.
Here are two triangles.
Triangle A
Triangle B
Are triangle A and triangle B similar triangles? You must give a reason for your answer.
The diagram shows a regular octagon ABCDEFGH.
Work out the size of angle HAC.
Also involves Tangent to a circle
B, D, E and F are points on a circle. ABC is the tangent to the circle at B.
Angle EDF = 40
Angle FBC = 70
Prove that the tangent ABC is parallel to EF. Give a reason for each stage of your working.
The diagram shows a quadrilateral ABCD drawn on a square grid.
Measure the length of BC.
Write down the mathematical name of quadrilateral ABCD.
Write down the order of rotational symmetry of quadrilateral ABCD.
On the diagram, mark an obtuse angle with the letter x.
Here is a diagram of a trapezium.
Work out the area of the trapezium.
The diagram shows a trapezium ABCD in which AB and DC are parallel.
AB = DB
Work out the value of x. Give a reason for each stage of your working.
The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF
CDF and ADE are straight lines. Angle BCD = 58°
Work out the size of angle DEF. Give a reason for each stage of your working.
The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF
CDF and ADE are straight lines. Angle BCD = 58°
Work out the size of angle DEF. Give a reason for each stage of your working.
ABDE is a quadrilateral. ABC is a triangle. DCB is a straight line.
Work out the value of x.
Give a reason for your answer.
Work out the value of y. Give a reason for each stage of your working.
A, B and C are points on a circle, centre O. Angle ABC = 38°
Work out the size of angle OAC. Give a reason for each stage of your working.
H is the point with coordinates (−4, 1) J is the point with coordinates (j, 15) where j <0 K is the point with coordinates (6, k)
M is the midpoint of JK. The gradient of HM is 2
Find the value of j and the value of k.
The diagram shows a line AB.
At the point A draw an acute angle. Label your acute angle a.
The diagram shows a circle with centre O.
Draw a diameter of the circle.
ABC is a triangle. D and E are points such that ACD and BCE are straight lines.
reflex angle ABC = 298° angle ECD = 97°
Work out the size of angle x. Give a reason for each stage of your working.
The diagram shows a triangle.
Work out the value of x.
The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y.
The two regular polygons each have n sides.
Work out the value of n.
The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y.
The two regular polygons each have n sides.
Work out the value of n.
Complete the following statements by writing a number on each dotted line.
A pentagon has........ sides.
The size of each angle in an equilateral triangle is........ °
1 kilometre =........ metres.
The diagram shows two triangles, CDB and BDA.
Angle ABC = 90° Angle CDB = 116° Angle DAB = 55°
Work out the size of the angle marked x. Give a reason for each stage of your working.
Also involves Pythagoras' theorem
A boat sails from point X to point Y and then to point Z.
Y is on a bearing of 280° from X. Z is on a bearing of 220° from Y.
The distance from X to Y is 3.5 km. The distance from Y to Z is 6 km.
Work out the bearing of Z from X. Give your answer correct to 1 decimal place.
ABCD is a quadrilateral. ADE is an equilateral triangle. DCF is a straight line.
Work out the size of angle EAB. Give a reason for each stage of your working.
ABC and DEF are parallel lines.
BG = BE Angle DEG = 38° Angle GEB = 65°
Find the size of angle ABG.
Also involves Coordinate geometry
The diagram shows a quadrilateral ABCD on a centimetre grid.
Work out the area of triangle ABC. You must include the units with your answer.
Give a reason why angle ACD is equal to angle CAB.
Write down an equation for the straight line that passes through D and C.
BCDE is a rectangle. ABE is an isosceles triangle.
AB = AE Angle BAE = 80
Work out the size of angle x.
The diagram shows a regular pentagon, ABCDE, a regular octagon, ABFGHIJK, and an isosceles triangle, BCF.
Work out the size of angle x.
The diagram shows a regular pentagon, ABCDE, a regular octagon, ABFGHIJK, and an isosceles triangle, BCF.
Work out the size of angle x.
Also involves Properties of triangles and quadrilaterals
The diagram shows a hexagon ABCDEF. BC is parallel to ED.
Work out the size of the obtuse angle DEF.
Memes
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