Mathematics 0580 · IGCSE
Angles
100 practice questions on Angles, with worked solutions and instant marking.
The diagram is NOT TO SCALE. It includes angles marked $63^\circ$, $58^\circ$, $a^\circ$ and $b^\circ$, and arrows are used to show the lines are parallel.
Feb/March 2018
The diagram displays four angles named A, B, C and D. Angle C is drawn as a reflex angle.
Feb/March 2019
The diagram displays a set of angles around one point. The angles given are $107\text{\u00b0}$, $124\text{\u00b0}$ and $x\text{\u00b0}$. The diagram carries the label NOT TO SCALE.
Feb/March 2020
Determine the interior angle of a regular polygon with 24 sides.
Feb/March 2020
State the mathematical name of this angle type.
Feb/March 2020
The towns $L$, $M$ and $N$ are marked on a map so that they make an equilateral triangle. The bearing of $M$ from $L$ is $103^{\circ}$. A diagram is provided, with North shown at $L$.
Feb/March 2021
Find the values of $a$, $b$ and $c$ here.
Feb/March 2021
Determine the size of one interior angle in a regular $9$-sided polygon.
Feb/March 2023
For a regular polygon, the interior angle and the exterior angle are related by the ratio interior : exterior = 11 : 1.
Feb/March 2023
From A, the bearing to B is $107^\circ$.
Feb/March 2024
Three regular polygons $A$, $B$ and $C$ are joined at one point. Their interior angles are in the ratio $a : b : c = 3 : 4 : 5$. The diagram labels the angles at the shared point as $a^\circ$, $b^\circ$ and $c^\circ$.
Feb/March 2025
Show that the interior angles of a pentagon add up to $540^\circ$.
Feb/March 2025
The diagram illustrates angle A, which is made by two straight lines.
Feb/March 2025
The diagram depicts a straight transversal cutting across two parallel lines. The angles at the upper intersection are marked $b$, $c$, $A$, $d$, and those at the lower intersection are marked $h$, $e$, $g$, $f$.
Feb/March 2025
The diagram shows $ABF$ parallel to $EDC$. Angle $EDA=37^\circ$, angle $ADB$ is a right angle, and $BC=BD$.
May/June 2015
ABCDE makes a pentagon.
May/June 2015
An isosceles triangle $ABE$ and a quadrilateral $BCDE$ are shown. $ABC$ is a straight line. The angle at $E$ inside triangle $ABE$ is $82^\circ$. The angle at $D$ is $102^\circ$. The angle at $C$ is $64^\circ$. It is marked NOT TO SCALE.
May/June 2015
A sketch contains two horizontal parallel lines that are intersected by one sloping line. The angle at the top intersection is labelled $124^\circ$, while the angle at the lower intersection is labelled $x^\circ$. The sketch is marked NOT TO SCALE.
May/June 2015
Triangle $ABC$ is isosceles, and $AC$ runs parallel to $BD$. In the diagram, angle $C$ is $40^\circ$, while the angles at $B$ are marked $a^\circ$ and $b^\circ$.
May/June 2016
The diagram consists of $5$ congruent kites.
May/June 2016
Each of the five angles in the hexagon measures $115^{\circ}$.
May/June 2016
The diagram depicts triangle $ABC$, which is isosceles, with $AC$ parallel to $BD$. The angle at $C$ is $40^{\circ}$. The points $A$, $B$, $C$, $D$ are labelled. At $B$, the angle between $AB$ and $AC$ is marked $a^{\circ}$, and the angle between $AC$ and $BD$ is marked $b^{\circ}$. The diagram is marked NOT TO SCALE.
May/June 2016
The interior angle of a regular polygon is $172^\circ$.
May/June 2016
A star diagram formed from 5 congruent kites is shown. The angles inside are labelled $x^{\circ}$, $y^{\circ}$ and $42^{\circ}$. The diagram is labelled NOT TO SCALE.
May/June 2016
The diagram depicts a transversal cutting across two parallel lines. One angle is labelled $70^\circ$, another is labelled $p^\circ$, and a further angle is labelled $q^\circ$. The diagram is NOT TO SCALE.
May/June 2017
A triangle has angles of $5x^\circ$, $6x^\circ$ and $7x^\circ$.
May/June 2017
A triangle has angles of $5x^{\circ}$, $6x^{\circ}$ and $7x^{\circ}$. The diagram labels these angles, and it is not drawn to scale.
May/June 2017
State the bearing of port P from port R.
May/June 2017
Determine the reflex angle at A.
May/June 2017
Find the values for $x$, $y$ and $z$.
May/June 2017
Calculate the size of one exterior angle in a regular octagon.
May/June 2018
The figure represents a quadrilateral. The angles indicated are $95^\circ$, $82^\circ$, $47^\circ$ and $x^\circ$. The diagram is labelled NOT TO SCALE.
May/June 2018
The diagram depicts two parallel lines $PAQ$ and $SBCT$. Also, $AB = AC$ and angle $QAC = 43^\circ$. The diagram is labelled NOT TO SCALE.
May/June 2018
The lighthouse lies on a bearing of $113^\circ$ from the coastguard station. Work out the bearing of the coastguard station from the lighthouse.
May/June 2018
The diagram depicts two parallel lines $PAQ$ and $SBCT$. It also gives $AB = AC$ and $ ngle QAC = 43^{\circ}$. The labelled points are $P, A, Q, C, T, S, B$. The angle at $A$ formed by $QA$ and $AC$ is marked $43^{\circ}$, while the angle at $A$ between $CA$ and $AB$ is marked $x^{\circ}$. NOT TO SCALE.
May/June 2018
On a map, towns A and B are shown. The bearing of A from B is $140^\circ$.
May/June 2018
The diagrams are not drawn to scale.
May/June 2018
The figure displays two parallel lines cut by one straight transversal. The angles are marked a, b, c, d, e, f, g and X.
May/June 2019
The drawings are not to scale. (a) Triangle ABC is isosceles. BCD lies on one straight line. The exterior angle at C is $118^\circ$. (b) A regular 10-sided polygon. (c) E, F and G are points on the circumference of a circle with centre O. JGH is tangent to the circle. The angle at G between the tangent and the chord is $58^\circ$. (d) In the diagram, AG and AF are straight lines. BC and DE are parallel. (e) PQR is a right-angled triangle with PQ = 21 cm, QR = 28 cm, and the right angle is at Q.
May/June 2019
Find the remaining two angles.
May/June 2019
The figure shows two parallel lines crossed by two straight lines. The angles indicated are 59^{\circ}, 37^{\circ}, $a^{\circ}$, $b^{\circ}$ and $c^{\circ}$. The figure is not drawn to scale.
May/June 2021
A quadrilateral is shown in a diagram. Its interior angles are marked as $4x^{\circ}$, $(3x+75)^{\circ}$, $(87-x)^{\circ}$, and one right angle ($90^{\circ}$). The drawing is not to scale.
May/June 2021
The diagram depicts two straight lines meeting at a vertex where the angle is marked $a$.
May/June 2021
A regular polygon has an exterior angle of $36^\circ$.
May/June 2021
The diagram depicts two parallel lines cut by a straight line. One angle is labelled $40^\circ$, and a second angle on the top line is marked $x$. The diagram is NOT TO SCALE.
May/June 2021
The figure contains three straight lines that intersect at a single point. Two of the angles are marked $y^\circ$ and the remaining angle is marked $100^\circ$. The figure is NOT TO SCALE.
May/June 2021
The sketch depicts two parallel lines crossed by two straight lines. The angles shown are 59^{\circ}, 37^{\circ}, and angles labelled a^{\circ}, b^{\circ}, and c^{\circ}. The sketch is not drawn to scale.
May/June 2021
The diagram depicts two parallel lines cut by a straight line. The angle at the top is marked $x$, and the matching angle below is $40^{\circ}$.
May/June 2021
The diagram depicts three straight lines intersecting at one point. One angle is $100^{\circ}$, and each of the other two angles is labelled $y^{\circ}$.
May/June 2021
The scale drawing indicates the location of town R on the map. The scale is 1 centimetre represents 5 kilometres. An arrow for north is drawn pointing upwards from R. Scale: 1 cm represents 5 km.
May/June 2021
Find the value of angle $ABC$.
May/June 2021
The diagram depicts two parallel lines intersected by a straight line.
May/June 2022
A diagram depicts points A and B, with North shown. NOT TO SCALE. The bearing from A to B is 059^{\circ}.
May/June 2022
The diagram shows A and B, with north indicated at both positions. A straight line connects A to B.
May/June 2022
PQRS is a quadrilateral. RST forms a straight line. The diagram marks the angles at R, Q and P as $73^{\circ}$, $129^{\circ}$ and $75^{\circ}$ respectively.
May/June 2022
A pentagon’s interior angles are given in the ratio $4 : 5 : 5 : 7 : 9$.
May/June 2022
In the diagram, $AB$ runs parallel to $PQ$. The lines $AQ$ and $PB$ meet at $X$, and $AX = XQ$.
May/June 2022
Points $A$ and $B$ are shown on a diagram. A vertical arrow indicates North. The bearing of $B$ from $A$ is $059^$. The diagram is not drawn to scale.
May/June 2022
The bearing of B from A is $x^{\circ}$. The bearing of A from B is $y^{\circ}$. The ratio $x : y$ is $2 : 7$. The diagram indicates north lines at A and B together with the angles $x^{\circ}$ and $y^{\circ}$. NOT TO SCALE.
May/June 2022
PQRS forms a quadrilateral, while RST lies on a straight line. The diagram marks the angles as follows: at R = 73^{\circ}, at Q = 129^{\circ}, and at P = 75^{\circ}. The points are labelled P, Q, R, S, T. NOT TO SCALE.
May/June 2022
Write down how many sides a hexagon has.
May/June 2022
State the geometric reason that explains why $x$ has the value 52.
May/June 2023
A right-angled triangle is shown, with angles marked $(3x - 1)^{\circ}$ and $4x^{\circ}$, together with a right angle. The diagram is labelled NOT TO SCALE.
May/June 2023
Work out the size of one interior angle in a regular 15-sided polygon.
May/June 2023
The diagram depicts triangle ABC, with ACD forming a straight line. The angle at A is $73^{\circ}$, the angle at B is $59^{\circ}$, and at C there are two neighbouring angles marked $x^{\circ}$ and $y^{\circ}$. The drawing is labelled NOT TO SCALE.
May/June 2023
The scale drawing indicates where town A and town B are located. A north arrow marked "North" is drawn at A. The diagram is NOT TO SCALE.
May/June 2023
Triangle $ABC$ is isosceles, with $AB = AC$ and $\angle BAC = 38^\circ$. The diagram is not drawn to scale.
May/June 2023
The diagram depicts a shape made by points B, A, C, D and E. The angle at B is $104^\circ$, the angle at A is $71^\circ$, and the angle at C is $56^\circ$. Points C, D and E are positioned on one straight horizontal line. The figure is labelled NOT TO SCALE. The note underneath says: CDE is a straight line.
May/June 2023
Draw a ring round the correct criterion for this statement: SAS, RHS, SSS, ASA.
May/June 2023
A straight line crosses two parallel lines. At the upper crossing, the angle shown is $58^\circ$. At the lower crossing, the angles are labelled $a^\circ$ and $b^\circ$. The diagram is not drawn to scale.
May/June 2023
State the mathematical name for this sort of angle.
May/June 2023
Calculate the bearing of B from C.
May/June 2023
Find the bearing of town C as measured from town B.
May/June 2024
The figure illustrates 5 kites that are congruent to kite $ABCD$. Each kite is connected to the following kite along one edge. Angle $DAB = 40^\circ$ and $DCE$ is a straight line.
May/June 2024
Three towns, A, B and C, are all the same distance apart from one another. The bearing of C from A is $104^\circ$.
May/June 2024
The diagram displays triangle $EFG$ together with a straight line $HFI$. Line $HFI$ is parallel to $EG$. The labels on the diagram include $\angle EFG = 105^{\circ}$, $\angle EGF = 52^{\circ}$, and angles marked $e^{\circ}$ and $f^{\circ}$.
May/June 2024
Write down the mathematical name of the angle marked $125^\circ$.
May/June 2024
Measure the size of angle $k$.
May/June 2024
Find the value of $a$ as well as the value of $b$.
May/June 2024
The diagram depicts two parallel lines crossed by two straight lines. The angles marked are $x^\circ$, $y^\circ$, $z^\circ$, $110^\circ$ and $50^\circ$. The drawing is not drawn to scale.
May/June 2025
The diagram presents two parallel lines cut by two straight lines. The angles indicated are labelled $w^{\circ}$, $x^{\circ}$, $y^{\circ}$, $76^{\circ}$ and $158^{\circ}$. It is marked NOT TO SCALE.
May/June 2025
The interior angle of a regular polygon measures $150^{\circ}$. Find how many sides this polygon has.
May/June 2025
The diagram depicts two straight lines that intersect two parallel lines.
May/June 2025
The figure contains points A, B, C, D, E and F. The angles marked on it are 104^{\circ}, 130^{\circ}, 70^{\circ}, 30^{\circ}, x^{\circ} at A and y^{\circ} at F. The markings indicate that AFB is an isosceles triangle. It is not drawn to scale.
May/June 2025
State the mathematical name of this kind of angle.
May/June 2025
A diagram shows points A, B, C, D and E. At B, the angle between BC and the horizontal BD is 53^{\circ}. The angle between the sloping line BE and BD is 32^{\circ}. At A on AE, the angle is marked $y^{\circ}$. At E on AE, the angle is marked $x^{\circ}$. ABC lies on one straight line. BD is parallel to AE.
May/June 2025
The diagram represents quadrilateral $ACDE$. Line $AC$ is parallel to $ED$, and point $B$ lies on $AC$. Also, $\angle EAB = 120^{\circ}$, $\angle ABE = 32^{\circ}$ and $\angle CBD = 64^{\circ}$.
Oct/Nov 2015
Find the size of one interior angle in a regular $15$-sided polygon.
Oct/Nov 2015
This scale diagram gives the locations of towns A and B on a map, and a north-pointing arrow is included. Town A is joined to town B by a straight line.
Oct/Nov 2015
The diagram depicts a quadrilateral with one side extended. The angles shown are 98^{\circ}, 66^{\circ}, 112^{\circ} and an exterior angle marked $x^{\circ}$. The diagram is NOT TO SCALE.
Oct/Nov 2015
Find the numerical value of $u$.
Oct/Nov 2015
Work out $x$.
Oct/Nov 2016
A diagram of intersecting lines with angles labelled $67^\circ$, $42^\circ$ and $a^\circ$; the diagram is marked "NOT TO SCALE".
Oct/Nov 2016
Calculate the perimeter of a regular octagon with side length 4 cm.
Oct/Nov 2016
Triangle $ABC$ is an isosceles triangle, with $AB = CB$. The angle $ABC$ measures $44^\circ$. The diagram is not drawn to scale.
Oct/Nov 2016
The diagram shows two straight lines crossing, with the angles labelled $67^{\circ}$, $42^{\circ}$ and $a^{\circ}$. The diagram is labelled "NOT TO SCALE".
Oct/Nov 2016
In triangle ABC, the equal sides are $AB$ and $CB$, so the triangle is isosceles. Angle $ABC = 44^\circ$. The diagram is NOT TO SCALE.
Oct/Nov 2016
The sketch represents a quadrilateral. NOT TO SCALE. Its interior angles are labelled 83^{\circ}, 104^{\circ}, 72^{\circ} and $x$^{\circ}.
Oct/Nov 2017
The figure depicts a regular pentagon. $AB$ serves as a line of symmetry. The angle at A formed with one side is marked $d$^{\circ}.
Oct/Nov 2017
Determine the measure of the interior angle of a regular hexagon.
Oct/Nov 2017